LMFDB - Embedded newform 572.2.e.b.131.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.10
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29936 + 0.558274i) q^{2} -0.726543i q^{3} +(1.37666 - 1.45079i) q^{4} +2.29501 q^{5} +(0.405610 + 0.944039i) q^{6} +3.79351 q^{7} +(-0.978833 + 2.65366i) q^{8} +2.47214 q^{9} +O(q^{10})$	\(q+(-1.29936 + 0.558274i) q^{2} -0.726543i q^{3} +(1.37666 - 1.45079i) q^{4} +2.29501 q^{5} +(0.405610 + 0.944039i) q^{6} +3.79351 q^{7} +(-0.978833 + 2.65366i) q^{8} +2.47214 q^{9} +(-2.98204 + 1.28125i) q^{10} +(2.55923 - 2.10958i) q^{11} +(-1.05406 - 1.00020i) q^{12} -1.00000i q^{13} +(-4.92913 + 2.11782i) q^{14} -1.66743i q^{15} +(-0.209612 - 3.99450i) q^{16} +5.71239i q^{17} +(-3.21219 + 1.38013i) q^{18} -7.93365 q^{19} +(3.15946 - 3.32960i) q^{20} -2.75615i q^{21} +(-2.14763 + 4.16985i) q^{22} +6.63587i q^{23} +(1.92799 + 0.711164i) q^{24} +0.267093 q^{25} +(0.558274 + 1.29936i) q^{26} -3.97574i q^{27} +(5.22238 - 5.50361i) q^{28} -8.31030i q^{29} +(0.930880 + 2.16658i) q^{30} +4.11349i q^{31} +(2.50239 + 5.07327i) q^{32} +(-1.53270 - 1.85939i) q^{33} +(-3.18908 - 7.42244i) q^{34} +8.70617 q^{35} +(3.40329 - 3.58656i) q^{36} -5.37803 q^{37} +(10.3087 - 4.42915i) q^{38} -0.726543 q^{39} +(-2.24644 + 6.09018i) q^{40} -0.997890i q^{41} +(1.53869 + 3.58122i) q^{42} -1.57946 q^{43} +(0.462624 - 6.61710i) q^{44} +5.67359 q^{45} +(-3.70463 - 8.62237i) q^{46} -4.83653i q^{47} +(-2.90218 + 0.152292i) q^{48} +7.39075 q^{49} +(-0.347049 + 0.149111i) q^{50} +4.15029 q^{51} +(-1.45079 - 1.37666i) q^{52} +4.83328 q^{53} +(2.21955 + 5.16591i) q^{54} +(5.87348 - 4.84152i) q^{55} +(-3.71322 + 10.0667i) q^{56} +5.76414i q^{57} +(4.63942 + 10.7981i) q^{58} +13.6011i q^{59} +(-2.41909 - 2.29548i) q^{60} -0.746606i q^{61} +(-2.29645 - 5.34489i) q^{62} +9.37808 q^{63} +(-6.08377 - 5.19497i) q^{64} -2.29501i q^{65} +(3.02958 + 1.56035i) q^{66} -2.18666i q^{67} +(8.28750 + 7.86402i) q^{68} +4.82124 q^{69} +(-11.3124 + 4.86043i) q^{70} +2.48648i q^{71} +(-2.41981 + 6.56020i) q^{72} -6.87525i q^{73} +(6.98799 - 3.00242i) q^{74} -0.194054i q^{75} +(-10.9219 + 11.5101i) q^{76} +(9.70848 - 8.00273i) q^{77} +(0.944039 - 0.405610i) q^{78} -6.78742 q^{79} +(-0.481062 - 9.16745i) q^{80} +4.52786 q^{81} +(0.557096 + 1.29662i) q^{82} +1.23912 q^{83} +(-3.99861 - 3.79428i) q^{84} +13.1100i q^{85} +(2.05229 - 0.881772i) q^{86} -6.03779 q^{87} +(3.09304 + 8.85625i) q^{88} -17.7307 q^{89} +(-7.37202 + 3.16742i) q^{90} -3.79351i q^{91} +(9.62729 + 9.13534i) q^{92} +2.98862 q^{93} +(2.70011 + 6.28438i) q^{94} -18.2079 q^{95} +(3.68595 - 1.81809i) q^{96} -5.11822 q^{97} +(-9.60323 + 4.12607i) q^{98} +(6.32677 - 5.21517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.29936	+	0.558274i	−0.918785	+	0.394759i
$2$	−1.29936	+	0.558274i	−0.918785	+	0.394759i
$3$		−	0.726543i		−	0.419470i	−0.977758	−	0.209735i	$-0.932740\pi$
$3$		−	0.726543i		−	0.419470i	0.977758	−	0.209735i	$-0.0672601\pi$
$4$	1.37666	−	1.45079i	0.688330	−	0.725397i
$5$	2.29501			1.02636			0.513181	−	0.858280i	$-0.328467\pi$
$5$	2.29501			1.02636			0.513181	+	0.858280i	$0.328467\pi$
$6$	0.405610	+	0.944039i	0.165589	+	0.385402i
$7$	3.79351			1.43381			0.716907	−	0.697169i	$-0.245557\pi$
$7$	3.79351			1.43381			0.716907	+	0.697169i	$0.245557\pi$
$8$	−0.978833	+	2.65366i	−0.346070	+	0.938209i
$9$	2.47214			0.824045
$10$	−2.98204	+	1.28125i	−0.943005	+	0.405166i
$11$	2.55923	−	2.10958i	0.771637	−	0.636063i
$11$	2.55923	−	2.10958i	0.771637	−	0.636063i
$12$	−1.05406	−	1.00020i	−0.304282	−	0.288734i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−4.92913	+	2.11782i	−1.31737	+	0.566011i
$15$		−	1.66743i		−	0.430528i
$16$	−0.209612	−	3.99450i	−0.0524029	−	0.998626i
$17$			5.71239i			1.38546i	0.721198	+	0.692729i	$0.243592\pi$
$17$			5.71239i			1.38546i	−0.721198	+	0.692729i	$0.756408\pi$
$18$	−3.21219	+	1.38013i	−0.757120	+	0.325299i
$19$	−7.93365			−1.82011			−0.910053	−	0.414493i	$-0.863959\pi$
$19$	−7.93365			−1.82011			−0.910053	+	0.414493i	$0.863959\pi$
$20$	3.15946	−	3.32960i	0.706476	−	0.744520i
$21$		−	2.75615i		−	0.601441i
$22$	−2.14763	+	4.16985i	−0.457877	+	0.889016i
$23$			6.63587i			1.38368i	0.722053	+	0.691838i	$0.243199\pi$
$23$			6.63587i			1.38368i	−0.722053	+	0.691838i	$0.756801\pi$
$24$	1.92799	+	0.711164i	0.393550	+	0.145166i
$25$	0.267093			0.0534185
$26$	0.558274	+	1.29936i	0.109487	+	0.254825i
$27$		−	3.97574i		−	0.765132i
$28$	5.22238	−	5.50361i	0.986937	−	1.04008i
$29$		−	8.31030i		−	1.54318i	−0.636118	−	0.771592i	$-0.719461\pi$
$29$		−	8.31030i		−	1.54318i	0.636118	−	0.771592i	$-0.280539\pi$
$30$	0.930880	+	2.16658i	0.169955	+	0.395562i
$31$			4.11349i			0.738804i	0.929270	+	0.369402i	$0.120438\pi$
$31$			4.11349i			0.738804i	−0.929270	+	0.369402i	$0.879562\pi$
$32$	2.50239	+	5.07327i	0.442364	+	0.896836i
$33$	−1.53270	−	1.85939i	−0.266809	−	0.323678i
$34$	−3.18908	−	7.42244i	−0.546922	−	1.27294i
$35$	8.70617			1.47161
$36$	3.40329	−	3.58656i	0.567215	−	0.597760i
$37$	−5.37803			−0.884143			−0.442072	−	0.896980i	$-0.645756\pi$
$37$	−5.37803			−0.884143			−0.442072	+	0.896980i	$0.645756\pi$
$38$	10.3087	−	4.42915i	1.67228	−	0.718503i
$39$	−0.726543			−0.116340
$40$	−2.24644	+	6.09018i	−0.355193	+	0.962942i
$41$		−	0.997890i		−	0.155844i	−0.996959	−	0.0779221i	$-0.975171\pi$
$41$		−	0.997890i		−	0.155844i	0.996959	−	0.0779221i	$-0.0248286\pi$
$42$	1.53869	+	3.58122i	0.237425	+	0.552595i
$43$	−1.57946			−0.240866			−0.120433	−	0.992721i	$-0.538428\pi$
$43$	−1.57946			−0.240866			−0.120433	+	0.992721i	$0.538428\pi$
$44$	0.462624	−	6.61710i	0.0697432	−	0.997565i
$45$	5.67359			0.845769
$46$	−3.70463	−	8.62237i	−0.546219	−	1.27130i
$47$		−	4.83653i		−	0.705481i	−0.935721	−	0.352740i	$-0.885250\pi$
$47$		−	4.83653i		−	0.705481i	0.935721	−	0.352740i	$-0.114750\pi$
$48$	−2.90218	+	0.152292i	−0.418893	+	0.0219814i
$49$	7.39075			1.05582
$50$	−0.347049	+	0.149111i	−0.0490801	+	0.0210875i
$51$	4.15029			0.581157
$52$	−1.45079	−	1.37666i	−0.201189	−	0.190908i
$53$	4.83328			0.663902			0.331951	−	0.943297i	$-0.392293\pi$
$53$	4.83328			0.663902			0.331951	+	0.943297i	$0.392293\pi$
$54$	2.21955	+	5.16591i	0.302043	+	0.702991i
$55$	5.87348	−	4.84152i	0.791979	−	0.652830i
$56$	−3.71322	+	10.0667i	−0.496200	+	1.34522i
$57$			5.76414i			0.763479i
$58$	4.63942	+	10.7981i	0.609186	+	1.41785i
$59$			13.6011i			1.77072i	0.464911	+	0.885358i	$0.346086\pi$
$59$			13.6011i			1.77072i	−0.464911	+	0.885358i	$0.653914\pi$
$60$	−2.41909	−	2.29548i	−0.312304	−	0.296345i
$61$		−	0.746606i		−	0.0955932i	−0.998857	−	0.0477966i	$-0.984780\pi$
$61$		−	0.746606i		−	0.0955932i	0.998857	−	0.0477966i	$-0.0152199\pi$
$62$	−2.29645	−	5.34489i	−0.291650	−	0.678802i
$63$	9.37808			1.18153
$64$	−6.08377	−	5.19497i	−0.760471	−	0.649372i
$65$		−	2.29501i		−	0.284662i
$66$	3.02958	+	1.56035i	0.372915	+	0.192065i
$67$		−	2.18666i		−	0.267143i	−0.991039	−	0.133571i	$-0.957355\pi$
$67$		−	2.18666i		−	0.267143i	0.991039	−	0.133571i	$-0.0426445\pi$
$68$	8.28750	+	7.86402i	1.00501	+	0.953653i
$69$	4.82124			0.580410
$70$	−11.3124	+	4.86043i	−1.35209	+	0.580932i
$71$			2.48648i			0.295091i	0.989055	+	0.147545i	$0.0471373\pi$
$71$			2.48648i			0.295091i	−0.989055	+	0.147545i	$0.952863\pi$
$72$	−2.41981	+	6.56020i	−0.285177	+	0.773126i
$73$		−	6.87525i		−	0.804687i	−0.915489	−	0.402344i	$-0.868196\pi$
$73$		−	6.87525i		−	0.804687i	0.915489	−	0.402344i	$-0.131804\pi$
$74$	6.98799	−	3.00242i	0.812337	−	0.349024i
$75$		−	0.194054i		−	0.0224074i
$76$	−10.9219	+	11.5101i	−1.25283	+	1.32030i
$77$	9.70848	−	8.00273i	1.10638	−	0.911995i
$78$	0.944039	−	0.405610i	0.106891	−	0.0459263i
$79$	−6.78742			−0.763644			−0.381822	−	0.924236i	$-0.624703\pi$
$79$	−6.78742			−0.763644			−0.381822	+	0.924236i	$0.624703\pi$
$80$	−0.481062	−	9.16745i	−0.0537843	−	1.02495i
$81$	4.52786			0.503096
$82$	0.557096	+	1.29662i	0.0615210	+	0.143187i
$83$	1.23912			0.136011			0.0680056	−	0.997685i	$-0.478336\pi$
$83$	1.23912			0.136011			0.0680056	+	0.997685i	$0.478336\pi$
$84$	−3.99861	−	3.79428i	−0.436284	−	0.413990i
$85$			13.1100i			1.42198i
$86$	2.05229	−	0.881772i	0.221304	−	0.0950840i
$87$	−6.03779			−0.647319
$88$	3.09304	+	8.85625i	0.329719	+	0.944079i
$89$	−17.7307			−1.87945			−0.939725	−	0.341932i	$-0.888919\pi$
$89$	−17.7307			−1.87945			−0.939725	+	0.341932i	$0.888919\pi$
$90$	−7.37202	+	3.16742i	−0.777079	+	0.333875i
$91$		−	3.79351i		−	0.397668i
$92$	9.62729	+	9.13534i	1.00371	+	0.952425i
$93$	2.98862			0.309906
$94$	2.70011	+	6.28438i	0.278495	+	0.648185i
$95$	−18.2079			−1.86809
$96$	3.68595	−	1.81809i	0.376195	−	0.185558i
$97$	−5.11822			−0.519677			−0.259838	−	0.965652i	$-0.583669\pi$
$97$	−5.11822			−0.519677			−0.259838	+	0.965652i	$0.583669\pi$
$98$	−9.60323	+	4.12607i	−0.970073	+	0.416796i
$99$	6.32677	−	5.21517i	0.635864	−	0.524144i
$100$	0.367696	−	0.387497i	0.0367696	−	0.0387497i
$101$		−	9.74743i		−	0.969906i	−0.874540	−	0.484953i	$-0.838837\pi$
$101$		−	9.74743i		−	0.969906i	0.874540	−	0.484953i	$-0.161163\pi$
$102$	−5.39272	+	2.31700i	−0.533958	+	0.229417i
$103$		−	7.63660i		−	0.752457i	−0.926527	−	0.376229i	$-0.877221\pi$
$103$		−	7.63660i		−	0.752457i	0.926527	−	0.376229i	$-0.122779\pi$
$104$	2.65366	+	0.978833i	0.260212	+	0.0959825i
$105$		−	6.32541i		−	0.617296i
$106$	−6.28016	+	2.69830i	−0.609983	+	0.262082i
$107$	2.88298			0.278708			0.139354	−	0.990243i	$-0.455497\pi$
$107$	2.88298			0.278708			0.139354	+	0.990243i	$0.455497\pi$
$108$	−5.76798	−	5.47324i	−0.555024	−	0.526663i
$109$		−	5.77915i		−	0.553542i	−0.960936	−	0.276771i	$-0.910736\pi$
$109$		−	5.77915i		−	0.553542i	0.960936	−	0.276771i	$-0.0892644\pi$
$110$	−4.92885	+	9.56987i	−0.469947	+	0.912452i
$111$			3.90737i			0.370871i
$112$	−0.795165	−	15.1532i	−0.0751360	−	1.43184i
$113$	9.34725			0.879315			0.439658	−	0.898165i	$-0.355100\pi$
$113$	9.34725			0.879315			0.439658	+	0.898165i	$0.355100\pi$
$114$	−3.21797	−	7.48968i	−0.301390	−	0.701472i
$115$			15.2294i			1.42015i
$116$	−12.0565	−	11.4405i	−1.11942	−	1.06222i
$117$		−	2.47214i		−	0.228549i
$118$	−7.59315	−	17.6727i	−0.699006	−	1.62691i
$119$			21.6700i			1.98649i
$120$	4.42477	+	1.63213i	0.403925	+	0.148993i
$121$	2.09934	−	10.7978i	0.190849	−	0.981619i
$122$	0.416811	+	0.970109i	0.0377363	+	0.0878295i
$123$	−0.725010			−0.0653719
$124$	5.96783	+	5.66288i	0.535927	+	0.508541i
$125$	−10.8621			−0.971535
$126$	−12.1855	+	5.23554i	−1.08557	+	0.466419i
$127$	1.30465			0.115769			0.0578846	−	0.998323i	$-0.481564\pi$
$127$	1.30465			0.115769			0.0578846	+	0.998323i	$0.481564\pi$
$128$	10.8052	+	3.35372i	0.955055	+	0.296430i
$129$			1.14755i			0.101036i
$130$	1.28125	+	2.98204i	0.112373	+	0.261543i
$131$	4.18831			0.365934			0.182967	−	0.983119i	$-0.441430\pi$
$131$	4.18831			0.365934			0.182967	+	0.983119i	$0.441430\pi$
$132$	−4.80760	−	0.336116i	−0.418448	−	0.0292552i
$133$	−30.0964			−2.60969
$134$	1.22075	+	2.84125i	0.105457	+	0.245447i
$135$		−	9.12438i		−	0.785302i
$136$	−15.1587	−	5.59148i	−1.29985	−	0.479465i
$137$	10.0701			0.860345			0.430172	−	0.902747i	$-0.358453\pi$
$137$	10.0701			0.860345			0.430172	+	0.902747i	$0.358453\pi$
$138$	−6.26452	+	2.69157i	−0.533271	+	0.229122i
$139$	−13.2656			−1.12518			−0.562588	−	0.826737i	$-0.690194\pi$
$139$	−13.2656			−1.12518			−0.562588	+	0.826737i	$0.690194\pi$
$140$	11.9854	−	12.6309i	1.01295	−	1.06750i
$141$	−3.51395			−0.295928
$142$	−1.38814	−	3.23083i	−0.116490	−	0.271125i
$143$	−2.10958	−	2.55923i	−0.176412	−	0.214014i
$144$	−0.518188	−	9.87496i	−0.0431824	−	0.822913i
$145$		−	19.0723i		−	1.58387i
$146$	3.83827	+	8.93341i	0.317658	+	0.739334i
$147$		−	5.36970i		−	0.442885i
$148$	−7.40373	+	7.80243i	−0.608583	+	0.641355i
$149$			19.6797i			1.61223i	0.591762	+	0.806113i	$0.298432\pi$
$149$			19.6797i			1.61223i	−0.591762	+	0.806113i	$0.701568\pi$
$150$	0.108335	+	0.252146i	0.00884555	+	0.0205876i
$151$	−5.62304			−0.457597			−0.228798	−	0.973474i	$-0.573480\pi$
$151$	−5.62304			−0.457597			−0.228798	+	0.973474i	$0.573480\pi$
$152$	7.76573	−	21.0532i	0.629884	−	1.70764i
$153$			14.1218i			1.14168i
$154$	−8.14708	+	15.8184i	−0.656510	+	1.27468i
$155$			9.44052i			0.758281i
$156$	−1.00020	+	1.05406i	−0.0800803	+	0.0843927i
$157$	8.44597			0.674062			0.337031	−	0.941494i	$-0.390577\pi$
$157$	8.44597			0.674062			0.337031	+	0.941494i	$0.390577\pi$
$158$	8.81928	−	3.78924i	0.701624	−	0.301456i
$159$		−	3.51159i		−	0.278487i
$160$	5.74302	+	11.6432i	0.454025	+	0.920478i
$161$			25.1733i			1.98393i
$162$	−5.88331	+	2.52779i	−0.462237	+	0.198602i
$163$		−	7.66727i		−	0.600547i	−0.953853	−	0.300274i	$-0.902922\pi$
$163$		−	7.66727i		−	0.600547i	0.953853	−	0.300274i	$-0.0970780\pi$
$164$	−1.44773	−	1.37376i	−0.113049	−	0.107272i
$165$	−3.51757	−	4.26733i	−0.273842	−	0.332211i
$166$	−1.61006	+	0.691769i	−0.124965	+	0.0536917i
$167$	−2.60657			−0.201703			−0.100851	−	0.994902i	$-0.532157\pi$
$167$	−2.60657			−0.201703			−0.100851	+	0.994902i	$0.532157\pi$
$168$	7.31387	+	2.69781i	0.564277	+	0.208141i
$169$	−1.00000			−0.0769231
$170$	−7.31898	−	17.0346i	−0.561340	−	1.30649i
$171$	−19.6131			−1.49985
$172$	−2.17438	+	2.29148i	−0.165795	+	0.174723i
$173$		−	11.5108i		−	0.875151i	−0.899182	−	0.437576i	$-0.855837\pi$
$173$		−	11.5108i		−	0.875151i	0.899182	−	0.437576i	$-0.144163\pi$
$174$	7.84525	−	3.37074i	0.594747	−	0.255535i
$175$	1.01322			0.0765922
$176$	−8.96317	−	9.78067i	−0.675625	−	0.737246i
$177$	9.88180			0.742761
$178$	23.0385	−	9.89858i	1.72681	−	0.741930i
$179$		−	6.03767i		−	0.451277i	−0.974211	−	0.225638i	$-0.927553\pi$
$179$		−	6.03767i		−	0.451277i	0.974211	−	0.225638i	$-0.0724468\pi$
$180$	7.81060	−	8.23121i	0.582168	−	0.613518i
$181$	−18.8800			−1.40334			−0.701668	−	0.712504i	$-0.747561\pi$
$181$	−18.8800			−1.40334			−0.701668	+	0.712504i	$0.747561\pi$
$182$	2.11782	+	4.92913i	0.156983	+	0.365372i
$183$	−0.542441			−0.0400984
$184$	−17.6093	−	6.49541i	−1.29818	−	0.478848i
$185$	−12.3427			−0.907451
$186$	−3.88329	+	1.66847i	−0.284737	+	0.122338i
$187$	12.0507	+	14.6193i	0.881238	+	1.06907i
$188$	−7.01682	−	6.65826i	−0.511754	−	0.485604i
$189$		−	15.0820i		−	1.09706i
$190$	23.6585	−	10.1650i	1.71637	−	0.737444i
$191$		−	20.6746i		−	1.49596i	−0.663720	−	0.747981i	$-0.731023\pi$
$191$		−	20.6746i		−	1.49596i	0.663720	−	0.747981i	$-0.268977\pi$
$192$	−3.77437	+	4.42012i	−0.272392	+	0.318995i
$193$			7.04365i			0.507013i	0.967334	+	0.253506i	$0.0815839\pi$
$193$			7.04365i			0.507013i	−0.967334	+	0.253506i	$0.918416\pi$
$194$	6.65040	−	2.85737i	0.477471	−	0.205147i
$195$	−1.66743			−0.119407
$196$	10.1746	−	10.7225i	0.726754	−	0.765891i
$197$			23.4388i			1.66994i	0.550294	+	0.834971i	$0.314516\pi$
$197$			23.4388i			1.66994i	−0.550294	+	0.834971i	$0.685484\pi$
$198$	−5.30924	+	10.3084i	−0.377311	+	0.732589i
$199$			22.2022i			1.57387i	0.617036	+	0.786935i	$0.288333\pi$
$199$			22.2022i			1.57387i	−0.617036	+	0.786935i	$0.711667\pi$
$200$	−0.261439	+	0.708772i	−0.0184865	+	0.0501177i
$201$	−1.58870			−0.112058
$202$	5.44174	+	12.6654i	0.382879	+	0.891134i
$203$		−	31.5253i		−	2.21264i
$204$	5.71355	−	6.02123i	0.400028	−	0.421570i
$205$		−	2.29017i		−	0.159953i
$206$	4.26332	+	9.92268i	0.297039	+	0.691346i
$207$			16.4048i			1.14021i
$208$	−3.99450	+	0.209612i	−0.276969	+	0.0145340i
$209$	−20.3041	+	16.7367i	−1.40446	+	1.15770i
$210$	3.53131	+	8.21896i	0.243683	+	0.567162i
$211$	17.1966			1.18386			0.591930	−	0.805989i	$-0.298366\pi$
$211$	17.1966			1.18386			0.591930	+	0.805989i	$0.298366\pi$
$212$	6.65379	−	7.01210i	0.456984	−	0.481593i
$213$	1.80653			0.123782
$214$	−3.74602	+	1.60949i	−0.256073	+	0.110023i
$215$	−3.62489			−0.247215
$216$	10.5502	+	3.89159i	0.717853	+	0.264789i
$217$			15.6046i			1.05931i
$218$	3.22635	+	7.50918i	0.218516	+	0.508586i
$219$	−4.99516			−0.337542
$220$	1.06173	−	15.1863i	0.0715818	−	1.02386i
$221$	5.71239			0.384257
$222$	−2.18138	−	5.07707i	−0.146405	−	0.340751i
$223$			1.84769i			0.123731i	0.998085	+	0.0618653i	$0.0197049\pi$
$223$			1.84769i			0.123731i	−0.998085	+	0.0618653i	$0.980295\pi$
$224$	9.49285	+	19.2455i	0.634267	+	1.28590i
$225$	0.660289			0.0440193
$226$	−12.1454	+	5.21833i	−0.807901	+	0.347118i
$227$	11.4140			0.757573			0.378787	−	0.925484i	$-0.376341\pi$
$227$	11.4140			0.757573			0.378787	+	0.925484i	$0.376341\pi$
$228$	8.36258	+	7.93526i	0.553826	+	0.525525i
$229$	−4.85025			−0.320514			−0.160257	−	0.987075i	$-0.551232\pi$
$229$	−4.85025			−0.320514			−0.160257	+	0.987075i	$0.551232\pi$
$230$	−8.50219	−	19.7885i	−0.560618	−	1.30481i
$231$	−5.81432	−	7.05363i	−0.382554	−	0.464095i
$232$	22.0527	+	8.13440i	1.44783	+	0.534050i
$233$			9.79816i			0.641899i	0.947096	+	0.320949i	$0.104002\pi$
$233$			9.79816i			0.641899i	−0.947096	+	0.320949i	$0.895998\pi$
$234$	1.38013	+	3.21219i	0.0902218	+	0.209987i
$235$		−	11.0999i		−	0.724078i
$236$	19.7324	+	18.7241i	1.28447	+	1.21884i
$237$			4.93135i			0.320325i
$238$	−12.0978	−	28.1571i	−0.784185	−	1.82516i
$239$	17.2587			1.11637			0.558187	−	0.829715i	$-0.311497\pi$
$239$	17.2587			1.11637			0.558187	+	0.829715i	$0.311497\pi$
$240$	−6.66054	+	0.349512i	−0.429936	+	0.0225609i
$241$		−	8.46691i		−	0.545402i	−0.962099	−	0.272701i	$-0.912083\pi$
$241$		−	8.46691i		−	0.545402i	0.962099	−	0.272701i	$-0.0879169\pi$
$242$	3.30035	+	15.2022i	0.212154	+	0.977236i
$243$		−	15.2169i		−	0.976165i
$244$	−1.08317	−	1.02782i	−0.0693430	−	0.0657997i
$245$	16.9619			1.08366
$246$	0.942047	−	0.404754i	0.0600627	−	0.0258062i
$247$			7.93365i			0.504806i
$248$	−10.9158	−	4.02642i	−0.693153	−	0.255678i
$249$		−	0.900274i		−	0.0570526i
$250$	14.1137	−	6.06402i	0.892631	−	0.383522i
$251$		−	13.1809i		−	0.831971i	−0.909371	−	0.415985i	$-0.863437\pi$
$251$		−	13.1809i		−	0.831971i	0.909371	−	0.415985i	$-0.136563\pi$
$252$	12.9104	−	13.6057i	0.813281	−	0.857077i
$253$	13.9989	+	16.9827i	0.880104	+	1.06770i
$254$	−1.69521	+	0.728354i	−0.106367	+	0.0457010i
$255$	9.52499			0.596478
$256$	−15.9121	+	1.67459i	−0.994508	+	0.104662i
$257$	−5.69070			−0.354976			−0.177488	−	0.984123i	$-0.556797\pi$
$257$	−5.69070			−0.354976			−0.177488	+	0.984123i	$0.556797\pi$
$258$	−0.640645	−	1.49107i	−0.0398848	−	0.0928302i
$259$	−20.4017			−1.26770
$260$	−3.32960	−	3.15946i	−0.206493	−	0.195941i
$261$		−	20.5442i		−	1.27165i
$262$	−5.44211	+	2.33822i	−0.336215	+	0.144456i
$263$	−9.67990			−0.596888			−0.298444	−	0.954427i	$-0.596468\pi$
$263$	−9.67990			−0.596888			−0.298444	+	0.954427i	$0.596468\pi$
$264$	6.43444	−	2.24722i	0.396012	−	0.138307i
$265$	11.0925			0.681404
$266$	39.1060	−	16.8021i	2.39774	−	1.03020i
$267$			12.8821i			0.788372i
$268$	−3.17239	−	3.01028i	−0.193785	−	0.183882i
$269$	10.3377			0.630300			0.315150	−	0.949042i	$-0.397945\pi$
$269$	10.3377			0.630300			0.315150	+	0.949042i	$0.397945\pi$
$270$	5.09390	+	11.8558i	0.310005	+	0.721523i
$271$	10.4997			0.637810			0.318905	−	0.947787i	$-0.396685\pi$
$271$	10.4997			0.637810			0.318905	+	0.947787i	$0.396685\pi$
$272$	22.8182	−	1.19738i	1.38355	−	0.0726020i
$273$	−2.75615			−0.166810
$274$	−13.0846	+	5.62186i	−0.790472	+	0.339629i
$275$	0.683552	−	0.563454i	0.0412197	−	0.0339775i
$276$	6.63722	−	6.99464i	0.399513	−	0.421028i
$277$			18.7238i			1.12500i	0.826796	+	0.562502i	$0.190161\pi$
$277$			18.7238i			1.12500i	−0.826796	+	0.562502i	$0.809839\pi$
$278$	17.2368	−	7.40586i	1.03380	−	0.444174i
$279$			10.1691i			0.608808i
$280$	−8.52189	+	23.1032i	−0.509280	+	1.38068i
$281$			6.83670i			0.407843i	0.978987	+	0.203922i	$0.0653688\pi$
$281$			6.83670i			0.407843i	−0.978987	+	0.203922i	$0.934631\pi$
$282$	4.56587	−	1.96174i	0.271894	−	0.116820i
$283$	3.23590			0.192355			0.0961773	−	0.995364i	$-0.469338\pi$
$283$	3.23590			0.192355			0.0961773	+	0.995364i	$0.469338\pi$
$284$	3.60737	+	3.42304i	0.214058	+	0.203120i
$285$			13.2288i			0.783605i
$286$	4.16985	+	2.14763i	0.246569	+	0.126992i
$287$		−	3.78551i		−	0.223452i
$288$	6.18624	+	12.5418i	0.364528	+	0.739033i
$289$	−15.6314			−0.919493
$290$	10.6475	+	24.7817i	0.625246	+	1.45523i
$291$			3.71861i			0.217989i
$292$	−9.97458	−	9.46488i	−0.583718	−	0.553890i
$293$			29.3894i			1.71694i	0.512860	+	0.858472i	$0.328586\pi$
$293$			29.3894i			1.71694i	−0.512860	+	0.858472i	$0.671414\pi$
$294$	2.99776	+	6.97716i	0.174833	+	0.406916i
$295$			31.2148i			1.81739i
$296$	5.26420	−	14.2714i	0.305975	−	0.829511i
$297$	−8.38715	−	10.1748i	−0.486672	−	0.590404i
$298$	−10.9867	−	25.5710i	−0.636441	−	1.48129i
$299$	6.63587			0.383762
$300$	−0.281533	−	0.267147i	−0.0162543	−	0.0154237i
$301$	−5.99171			−0.345357
$302$	7.30634	−	3.13920i	0.420433	−	0.180641i
$303$	−7.08192			−0.406846
$304$	1.66299	+	31.6910i	0.0953788	+	1.81760i
$305$		−	1.71347i		−	0.0981132i
$306$	−7.88383	−	18.3493i	−0.450689	−	1.04896i
$307$	5.65840			0.322942			0.161471	−	0.986877i	$-0.448376\pi$
$307$	5.65840			0.322942			0.161471	+	0.986877i	$0.448376\pi$
$308$	1.75497	−	25.1021i	0.0999988	−	1.43032i
$309$	−5.54832			−0.315633
$310$	−5.27039	−	12.2666i	−0.299338	−	0.696697i
$311$		−	16.0544i		−	0.910364i	−0.890398	−	0.455182i	$-0.849574\pi$
$311$		−	16.0544i		−	0.910364i	0.890398	−	0.455182i	$-0.150426\pi$
$312$	0.711164	−	1.92799i	0.0402617	−	0.109151i
$313$	28.0858			1.58750			0.793750	−	0.608244i	$-0.208126\pi$
$313$	28.0858			1.58750			0.793750	+	0.608244i	$0.208126\pi$
$314$	−10.9743	+	4.71516i	−0.619318	+	0.266092i
$315$	21.5228			1.21267
$316$	−9.34397	+	9.84715i	−0.525639	+	0.553945i
$317$	−31.8707			−1.79004			−0.895019	−	0.446029i	$-0.852838\pi$
$317$	−31.8707			−1.79004			−0.895019	+	0.446029i	$0.852838\pi$
$318$	1.96043	+	4.56281i	0.109935	+	0.255869i
$319$	−17.5313	−	21.2680i	−0.981562	−	1.19078i
$320$	−13.9623	−	11.9225i	−0.780519	−	0.666490i
$321$		−	2.09461i		−	0.116910i
$322$	−14.0536	−	32.7091i	−0.783176	−	1.82281i
$323$		−	45.3201i		−	2.52168i
$324$	6.23333	−	6.56900i	0.346296	−	0.364944i
$325$		−	0.267093i		−	0.0148156i
$326$	4.28044	+	9.96253i	0.237072	+	0.551773i
$327$	−4.19880			−0.232194
$328$	2.64806	+	0.976768i	0.146214	+	0.0539330i
$329$		−	18.3475i		−	1.01153i
$330$	6.95292	+	3.58102i	0.382746	+	0.197129i
$331$			11.6679i			0.641325i	0.947194	+	0.320662i	$0.103905\pi$
$331$			11.6679i			0.641325i	−0.947194	+	0.320662i	$0.896095\pi$
$332$	1.70585	−	1.79771i	0.0936206	−	0.0986622i
$333$	−13.2952			−0.728574
$334$	3.38687	−	1.45518i	0.185321	−	0.0796240i
$335$		−	5.01841i		−	0.274185i
$336$	−11.0095	+	0.577721i	−0.600615	+	0.0315173i
$337$		−	14.6357i		−	0.797258i	−0.917112	−	0.398629i	$-0.869486\pi$
$337$		−	14.6357i		−	0.797258i	0.917112	−	0.398629i	$-0.130514\pi$
$338$	1.29936	−	0.558274i	0.0706757	−	0.0303661i
$339$		−	6.79118i		−	0.368846i
$340$	19.0199	+	18.0480i	1.03150	+	0.978793i
$341$	8.67774	+	10.5274i	0.469926	+	0.570089i
$342$	25.4844	−	10.9495i	1.37804	−	0.592079i
$343$	1.48233			0.0800384
$344$	1.54603	−	4.19135i	0.0833564	−	0.225982i
$345$	11.0648			0.595710
$346$	6.42619	+	14.9567i	0.345474	+	0.804076i
$347$	28.9804			1.55575			0.777876	−	0.628418i	$-0.216297\pi$
$347$	28.9804			1.55575			0.777876	+	0.628418i	$0.216297\pi$
$348$	−8.31198	+	8.75959i	−0.445569	+	0.469563i
$349$		−	14.5362i		−	0.778106i	−0.921215	−	0.389053i	$-0.872802\pi$
$349$		−	14.5362i		−	0.778106i	0.921215	−	0.389053i	$-0.127198\pi$
$350$	−1.31654	+	0.565654i	−0.0703718	+	0.0302355i
$351$	−3.97574			−0.212209
$352$	17.1067	+	7.70468i	0.911788	+	0.410661i
$353$	−34.2402			−1.82242			−0.911210	−	0.411942i	$-0.864851\pi$
$353$	−34.2402			−1.82242			−0.911210	+	0.411942i	$0.864851\pi$
$354$	−12.8400	+	5.51675i	−0.682438	+	0.293212i
$355$			5.70651i			0.302870i
$356$	−24.4091	+	25.7236i	−1.29368	+	1.36335i
$357$	15.7442			0.833271
$358$	3.37068	+	7.84510i	0.178146	+	0.414626i
$359$	−20.7178			−1.09344			−0.546722	−	0.837315i	$-0.684124\pi$
$359$	−20.7178			−1.09344			−0.546722	+	0.837315i	$0.684124\pi$
$360$	−5.55350	+	15.0557i	−0.292695	+	0.793507i
$361$	43.9429			2.31278
$362$	24.5318	−	10.5402i	1.28936	−	0.553980i
$363$	−7.84507	−	1.52526i	−0.411760	−	0.0800552i
$364$	−5.50361	−	5.22238i	−0.288468	−	0.273727i
$365$		−	15.7788i		−	0.825900i
$366$	0.704825	−	0.302831i	0.0368418	−	0.0158292i
$367$			20.5032i			1.07026i	0.844770	+	0.535130i	$0.179737\pi$
$367$			20.5032i			1.07026i	−0.844770	+	0.535130i	$0.820263\pi$
$368$	26.5070	−	1.39096i	1.38177	−	0.0725086i
$369$		−	2.46692i		−	0.128423i
$370$	16.0375	−	6.89059i	0.833752	−	0.358225i
$371$	18.3351			0.951912
$372$	4.11432	−	4.33588i	0.213318	−	0.224805i
$373$			5.86879i			0.303875i	0.988390	+	0.151937i	$0.0485512\pi$
$373$			5.86879i			0.303875i	−0.988390	+	0.151937i	$0.951449\pi$
$374$	−23.8198	−	12.2681i	−1.23169	−	0.634369i
$375$			7.89177i			0.407529i
$376$	12.8345	+	4.73416i	0.661888	+	0.244146i
$377$	−8.31030			−0.428002
$378$	8.41990	+	19.5969i	0.433073	+	1.00796i
$379$		−	33.0314i		−	1.69671i	−0.529428	−	0.848355i	$-0.677593\pi$
$379$		−	33.0314i		−	1.69671i	0.529428	−	0.848355i	$-0.322407\pi$
$380$	−25.0660	+	26.4159i	−1.28586	+	1.35511i
$381$		−	0.947887i		−	0.0485617i
$382$	11.5421	+	26.8637i	0.590545	+	1.37447i
$383$			24.3041i			1.24188i	0.783857	+	0.620941i	$0.213249\pi$
$383$			24.3041i			1.24188i	−0.783857	+	0.620941i	$0.786751\pi$
$384$	2.43662	−	7.85045i	0.124343	−	0.400616i
$385$	22.2811	−	18.3664i	1.13555	−	0.936037i
$386$	−3.93229	−	9.15222i	−0.200148	−	0.465836i
$387$	−3.90464			−0.198484
$388$	−7.04605	+	7.42549i	−0.357709	+	0.376972i
$389$	16.2901			0.825940			0.412970	−	0.910745i	$-0.364491\pi$
$389$	16.2901			0.825940			0.412970	+	0.910745i	$0.364491\pi$
$390$	2.16658	−	0.930880i	0.109709	−	0.0471370i
$391$	−37.9067			−1.91702
$392$	−7.23432	+	19.6125i	−0.365388	+	0.990581i
$393$		−	3.04299i		−	0.153498i
$394$	−13.0852	−	30.4553i	−0.659225	−	1.53432i
$395$	−15.5772			−0.783775
$396$	1.14367	−	16.3584i	0.0574716	−	0.822039i
$397$	6.20892			0.311617			0.155808	−	0.987787i	$-0.450202\pi$
$397$	6.20892			0.311617			0.155808	+	0.987787i	$0.450202\pi$
$398$	−12.3949	−	28.8486i	−0.621300	−	1.44605i
$399$			21.8663i			1.09469i
$400$	−0.0559857	−	1.06690i	−0.00279929	−	0.0533451i
$401$	9.45444			0.472132			0.236066	−	0.971737i	$-0.424142\pi$
$401$	9.45444			0.472132			0.236066	+	0.971737i	$0.424142\pi$
$402$	2.06429	−	0.886929i	0.102957	−	0.0442360i
$403$	4.11349			0.204907
$404$	−14.1415	−	13.4189i	−0.703567	−	0.667615i
$405$	10.3915			0.516358
$406$	17.5997	+	40.9626i	0.873460	+	2.03294i
$407$	−13.7636	+	11.3454i	−0.682238	+	0.562371i
$408$	−4.06245	+	11.0134i	−0.201121	+	0.545247i
$409$			3.42030i			0.169123i	0.996418	+	0.0845614i	$0.0269489\pi$
$409$			3.42030i			0.169123i	−0.996418	+	0.0845614i	$0.973051\pi$
$410$	1.27854	+	2.97575i	0.0631428	+	0.146962i
$411$		−	7.31634i		−	0.360889i
$412$	−11.0791	−	10.5130i	−0.545830	−	0.517939i
$413$			51.5961i			2.53888i
$414$	−9.15836	−	21.3157i	−0.450109	−	1.04761i
$415$	2.84380			0.139597
$416$	5.07327	−	2.50239i	0.248737	−	0.122690i
$417$			9.63805i			0.471977i
$418$	17.0386	−	33.0822i	0.833384	−	1.61810i
$419$			8.40727i			0.410722i	0.978686	+	0.205361i	$0.0658369\pi$
$419$			8.40727i			0.410722i	−0.978686	+	0.205361i	$0.934163\pi$
$420$	−9.17687	−	8.70794i	−0.447785	−	0.424904i
$421$	−36.6331			−1.78539			−0.892693	−	0.450665i	$-0.851187\pi$
$421$	−36.6331			−1.78539			−0.892693	+	0.450665i	$0.851187\pi$
$422$	−22.3445	+	9.60039i	−1.08771	+	0.467340i
$423$		−	11.9566i		−	0.581348i
$424$	−4.73098	+	12.8259i	−0.229757	+	0.622879i
$425$			1.52574i			0.0740091i
$426$	−2.34733	+	1.00854i	−0.113729	+	0.0488640i
$427$		−	2.83226i		−	0.137063i
$428$	3.96888	−	4.18261i	0.191843	−	0.202174i
$429$	−1.85939	+	1.53270i	−0.0897722	+	0.0739995i
$430$	4.71003	−	2.02368i	0.227138	−	0.0975905i
$431$	17.5158			0.843707			0.421854	−	0.906664i	$-0.361380\pi$
$431$	17.5158			0.843707			0.421854	+	0.906664i	$0.361380\pi$
$432$	−15.8811	+	0.833361i	−0.764080	+	0.0400951i
$433$	−0.930036			−0.0446947			−0.0223473	−	0.999750i	$-0.507114\pi$
$433$	−0.930036			−0.0446947			−0.0223473	+	0.999750i	$0.507114\pi$
$434$	−8.71163	−	20.2759i	−0.418172	−	0.973276i
$435$	−13.8568			−0.664383
$436$	−8.38436	−	7.95593i	−0.401538	−	0.381020i
$437$		−	52.6467i		−	2.51843i
$438$	6.49050	−	2.78867i	0.310128	−	0.133248i
$439$	−14.7686			−0.704867			−0.352433	−	0.935837i	$-0.614646\pi$
$439$	−14.7686			−0.704867			−0.352433	+	0.935837i	$0.614646\pi$
$440$	7.09857	+	20.3252i	0.338411	+	0.968967i
$441$	18.2709			0.870045
$442$	−7.42244	+	3.18908i	−0.353049	+	0.151689i
$443$		−	6.56821i		−	0.312065i	−0.987752	−	0.156032i	$-0.950130\pi$
$443$		−	6.56821i		−	0.312065i	0.987752	−	0.156032i	$-0.0498705\pi$
$444$	5.66879	+	5.37912i	0.269029	+	0.255282i
$445$	−40.6922			−1.92900
$446$	−1.03152	−	2.40081i	−0.0488438	−	0.113682i
$447$	14.2982			0.676279
$448$	−23.0789	−	19.7072i	−1.09037	−	0.931078i
$449$	−33.7654			−1.59349			−0.796745	−	0.604316i	$-0.793446\pi$
$449$	−33.7654			−1.59349			−0.796745	+	0.604316i	$0.793446\pi$
$450$	−0.857952	+	0.368622i	−0.0404442	+	0.0173770i
$451$	−2.10513	−	2.55383i	−0.0991267	−	0.120255i
$452$	12.8680	−	13.5609i	0.605259	−	0.637853i
$453$			4.08538i			0.191948i
$454$	−14.8309	+	6.37213i	−0.696047	+	0.299059i
$455$		−	8.70617i		−	0.408152i
$456$	−15.2960	−	5.64213i	−0.716302	−	0.264217i
$457$		−	41.0828i		−	1.92177i	−0.276940	−	0.960887i	$-0.589320\pi$
$457$		−	41.0828i		−	1.92177i	0.276940	−	0.960887i	$-0.410680\pi$
$458$	6.30222	−	2.70777i	0.294483	−	0.126526i
$459$	22.7110			1.06006
$460$	22.0948	+	20.9657i	1.03017	+	0.977533i
$461$			37.2995i			1.73721i	0.495504	+	0.868606i	$0.334983\pi$
$461$			37.2995i			1.73721i	−0.495504	+	0.868606i	$0.665017\pi$
$462$	11.4927	+	5.91920i	0.534691	+	0.275386i
$463$			14.0399i			0.652490i	0.945285	+	0.326245i	$0.105783\pi$
$463$			14.0399i			0.652490i	−0.945285	+	0.326245i	$0.894217\pi$
$464$	−33.1955	+	1.74194i	−1.54106	+	0.0808674i
$465$	6.85894			0.318076
$466$	−5.47006	−	12.7313i	−0.253395	−	0.589767i
$467$		−	2.48028i		−	0.114774i	−0.998352	−	0.0573869i	$-0.981723\pi$
$467$		−	2.48028i		−	0.114774i	0.998352	−	0.0573869i	$-0.0182768\pi$
$468$	−3.58656	−	3.40329i	−0.165789	−	0.157317i
$469$		−	8.29511i		−	0.383033i
$470$	6.19679	+	14.4228i	0.285837	+	0.665272i
$471$		−	6.13636i		−	0.282748i
$472$	−36.0927	−	13.3132i	−1.66130	−	0.612791i
$473$	−4.04221	+	3.33200i	−0.185861	+	0.153206i
$474$	−2.75304	−	6.40758i	−0.126451	−	0.294310i
$475$	−2.11902			−0.0972273
$476$	31.4388	+	29.8323i	1.44099	+	1.36736i
$477$	11.9485			0.547086
$478$	−22.4252	+	9.63509i	−1.02571	+	0.440699i
$479$	−28.1081			−1.28429			−0.642145	−	0.766583i	$-0.721955\pi$
$479$	−28.1081			−1.28429			−0.642145	+	0.766583i	$0.721955\pi$
$480$	8.45930	−	4.17255i	0.386112	−	0.190450i
$481$			5.37803i			0.245217i
$482$	4.72685	+	11.0015i	0.215302	+	0.501107i
$483$	18.2895			0.832199
$484$	−12.7753	−	17.9106i	−0.580697	−	0.814120i
$485$	−11.7464			−0.533376
$486$	8.49520	+	19.7722i	0.385350	+	0.896885i
$487$			28.1869i			1.27727i	0.769510	+	0.638635i	$0.220501\pi$
$487$			28.1869i			1.27727i	−0.769510	+	0.638635i	$0.779499\pi$
$488$	1.98124	+	0.730803i	0.0896863	+	0.0330819i
$489$	−5.57060			−0.251911
$490$	−22.0396	+	9.46938i	−0.995646	+	0.427783i
$491$	−4.19896			−0.189496			−0.0947482	−	0.995501i	$-0.530205\pi$
$491$	−4.19896			−0.189496			−0.0947482	+	0.995501i	$0.530205\pi$
$492$	−0.998092	+	1.05184i	−0.0449975	+	0.0474206i
$493$	47.4717			2.13802
$494$	−4.42915	−	10.3087i	−0.199277	−	0.463808i
$495$	14.5200	−	11.9689i	0.652627	−	0.537962i
$496$	16.4313	−	0.862235i	0.737789	−	0.0387155i
$497$			9.43250i			0.423106i
$498$	0.502600	+	1.16978i	0.0225220	+	0.0524190i
$499$		−	40.2736i		−	1.80290i	−0.432888	−	0.901448i	$-0.642506\pi$
$499$		−	40.2736i		−	1.80290i	0.432888	−	0.901448i	$-0.357494\pi$
$500$	−14.9534	+	15.7587i	−0.668737	+	0.704749i
$501$			1.89379i			0.0846082i
$502$	7.35855	+	17.1267i	0.328428	+	0.764402i
$503$	−22.7646			−1.01502			−0.507511	−	0.861645i	$-0.669434\pi$
$503$	−22.7646			−1.01502			−0.507511	+	0.861645i	$0.669434\pi$
$504$	−9.17958	+	24.8862i	−0.408891	+	1.10852i
$505$		−	22.3705i		−	0.995474i
$506$	−27.6706	−	14.2514i	−1.23011	−	0.633553i
$507$			0.726543i			0.0322669i
$508$	1.79607	−	1.89278i	0.0796875	−	0.0839788i
$509$	−30.5183			−1.35270			−0.676351	−	0.736580i	$-0.736440\pi$
$509$	−30.5183			−1.35270			−0.676351	+	0.736580i	$0.736440\pi$
$510$	−12.3764	+	5.31755i	−0.548035	+	0.235465i
$511$		−	26.0814i		−	1.15377i
$512$	19.7407	−	11.0592i	0.872422	−	0.488753i
$513$			31.5421i			1.39262i
$514$	7.39425	−	3.17697i	0.326147	−	0.140130i
$515$		−	17.5261i		−	0.772293i
$516$	1.66485	+	1.57978i	0.0732911	+	0.0695460i
$517$	−10.2031	−	12.3778i	−0.448730	−	0.544375i
$518$	26.5090	−	11.3897i	1.16474	−	0.500435i
$519$	−8.36310			−0.367099
$520$	6.09018	+	2.24644i	0.267072	+	0.0985128i
$521$	38.6535			1.69344			0.846721	−	0.532038i	$-0.178574\pi$
$521$	38.6535			1.69344			0.846721	+	0.532038i	$0.178574\pi$
$522$	11.4693	+	26.6943i	0.501997	+	1.16838i
$523$	39.2314			1.71547			0.857734	−	0.514093i	$-0.171871\pi$
$523$	39.2314			1.71547			0.857734	+	0.514093i	$0.171871\pi$
$524$	5.76588	−	6.07638i	0.251884	−	0.265448i
$525$		−	0.736147i		−	0.0321281i
$526$	12.5776	−	5.40403i	0.548411	−	0.235627i
$527$	−23.4978			−1.02358
$528$	−7.10607	+	6.51213i	−0.309252	+	0.283404i
$529$	−21.0348			−0.914557
$530$	−14.4131	+	6.19263i	−0.626063	+	0.268991i
$531$			33.6238i			1.45915i
$532$	−41.4326	+	43.6638i	−1.79633	+	1.89306i
$533$	−0.997890			−0.0432234
$534$	−7.19174	−	16.7385i	−0.311217	−	0.724344i
$535$	6.61648			0.286055
$536$	5.80263	+	2.14037i	0.250636	+	0.0924500i
$537$	−4.38663			−0.189297
$538$	−13.4324	+	5.77126i	−0.579110	+	0.248817i
$539$	18.9147	−	15.5914i	0.814712	−	0.671569i
$540$	−13.2376	−	12.5612i	−0.569656	−	0.540547i
$541$		−	27.0000i		−	1.16082i	−0.814324	−	0.580411i	$-0.802892\pi$
$541$		−	27.0000i		−	1.16082i	0.814324	−	0.580411i	$-0.197108\pi$
$542$	−13.6428	+	5.86170i	−0.586010	+	0.251782i
$543$			13.7171i			0.588657i
$544$	−28.9805	+	14.2946i	−1.24253	+	0.612876i
$545$		−	13.2632i		−	0.568135i
$546$	3.58122	−	1.53869i	0.153262	−	0.0658497i
$547$	−13.2668			−0.567248			−0.283624	−	0.958936i	$-0.591537\pi$
$547$	−13.2668			−0.567248			−0.283624	+	0.958936i	$0.591537\pi$
$548$	13.8631	−	14.6096i	0.592201	−	0.624092i
$549$		−	1.84571i		−	0.0787731i
$550$	−0.573617	+	1.11374i	−0.0244591	+	0.0474899i
$551$			65.9311i			2.80876i
$552$	−4.71920	+	12.7939i	−0.200862	+	0.544545i
$553$	−25.7482			−1.09492
$554$	−10.4530	−	24.3289i	−0.444106	−	1.03364i
$555$			8.96747i			0.380648i
$556$	−18.2623	+	19.2457i	−0.774493	+	0.816200i
$557$		−	7.26714i		−	0.307919i	−0.988077	−	0.153959i	$-0.950798\pi$
$557$		−	7.26714i		−	0.307919i	0.988077	−	0.153959i	$-0.0492025\pi$
$558$	−5.67714	−	13.2133i	−0.240333	−	0.559364i
$559$			1.57946i			0.0668041i
$560$	−1.82492	−	34.7768i	−0.0771167	−	1.46959i
$561$	10.6216	−	8.75538i	0.448443	−	0.369652i
$562$	−3.81675	−	8.88332i	−0.161000	−	0.374720i
$563$	8.00324			0.337296			0.168648	−	0.985676i	$-0.446060\pi$
$563$	8.00324			0.337296			0.168648	+	0.985676i	$0.446060\pi$
$564$	−4.83751	+	5.09802i	−0.203696	+	0.214665i
$565$	21.4521			0.902496
$566$	−4.20460	+	1.80652i	−0.176732	+	0.0759337i
$567$	17.1765			0.721346
$568$	−6.59826	−	2.43385i	−0.276857	−	0.102122i
$569$			22.8243i			0.956844i	0.878130	+	0.478422i	$0.158791\pi$
$569$			22.8243i			0.956844i	−0.878130	+	0.478422i	$0.841209\pi$
$570$	−7.38528	−	17.1889i	−0.309335	−	0.719965i
$571$	4.05779			0.169813			0.0849065	−	0.996389i	$-0.472941\pi$
$571$	4.05779			0.169813			0.0849065	+	0.996389i	$0.472941\pi$
$572$	−6.61710	−	0.462624i	−0.276675	−	0.0193433i
$573$	−15.0210			−0.627511
$574$	2.11335	+	4.91873i	0.0882096	+	0.205304i
$575$			1.77239i			0.0739139i
$576$	−15.0399	−	12.8427i	−0.626663	−	0.535112i
$577$	9.61946			0.400463			0.200232	−	0.979749i	$-0.435830\pi$
$577$	9.61946			0.400463			0.200232	+	0.979749i	$0.435830\pi$
$578$	20.3108	−	8.72659i	0.844816	−	0.362978i
$579$	5.11751			0.212677
$580$	−27.6699	−	26.2560i	−1.14893	−	1.09022i
$581$	4.70062			0.195015
$582$	−2.07600	−	4.83180i	−0.0860530	−	0.200284i
$583$	12.3695	−	10.1962i	0.512292	−	0.422283i
$584$	18.2445	+	6.72972i	0.754964	+	0.278478i
$585$		−	5.67359i		−	0.234574i
$586$	−16.4073	−	38.1873i	−0.677780	−	1.57750i
$587$		−	16.1560i		−	0.666830i	−0.942780	−	0.333415i	$-0.891799\pi$
$587$		−	16.1560i		−	0.666830i	0.942780	−	0.333415i	$-0.108201\pi$
$588$	−7.79033	−	7.39225i	−0.321268	−	0.304851i
$589$		−	32.6350i		−	1.34470i
$590$	−17.4264	−	40.5592i	−0.717433	−	1.66979i
$591$	17.0293			0.700490
$592$	1.12730	+	21.4826i	0.0463317	+	0.882929i
$593$			19.3091i			0.792928i	0.918050	+	0.396464i	$0.129763\pi$
$593$			19.3091i			0.792928i	−0.918050	+	0.396464i	$0.870237\pi$
$594$	16.5782	+	8.53843i	0.680214	+	0.350336i
$595$			49.7330i			2.03886i
$596$	28.5512	+	27.0923i	1.16950	+	1.10974i
$597$	16.1308			0.660191
$598$	−8.62237	+	3.70463i	−0.352595	+	0.151494i
$599$			39.4563i			1.61214i	0.591821	+	0.806070i	$0.298409\pi$
$599$			39.4563i			1.61214i	−0.591821	+	0.806070i	$0.701591\pi$
$600$	0.514953	+	0.189947i	0.0210229	+	0.00775454i
$601$		−	27.8312i		−	1.13526i	−0.823285	−	0.567629i	$-0.807861\pi$
$601$		−	27.8312i		−	1.13526i	0.823285	−	0.567629i	$-0.192139\pi$
$602$	7.78538	−	3.34502i	0.317308	−	0.136333i
$603$		−	5.40571i		−	0.220138i
$604$	−7.74102	+	8.15788i	−0.314978	+	0.331940i
$605$	4.81801	−	24.7811i	0.195880	−	1.00750i
$606$	9.20195	−	3.95365i	0.373804	−	0.160606i
$607$	33.7594			1.37025			0.685125	−	0.728425i	$-0.259747\pi$
$607$	33.7594			1.37025			0.685125	+	0.728425i	$0.259747\pi$
$608$	−19.8531	−	40.2496i	−0.805149	−	1.63234i
$609$	−22.9044			−0.928135
$610$	0.956587	+	2.22641i	0.0387311	+	0.0901449i
$611$	−4.83653			−0.195665
$612$	20.4878	+	19.4409i	0.828172	+	0.785853i
$613$		−	24.3558i		−	0.983721i	−0.870674	−	0.491861i	$-0.836317\pi$
$613$		−	24.3558i		−	0.983721i	0.870674	−	0.491861i	$-0.163683\pi$
$614$	−7.35229	+	3.15894i	−0.296714	+	0.127484i
$615$	−1.66391			−0.0670953
$616$	11.7335	+	33.5963i	0.472756	+	1.35363i
$617$	36.1729			1.45627			0.728133	−	0.685436i	$-0.240388\pi$
$617$	36.1729			1.45627			0.728133	+	0.685436i	$0.240388\pi$
$618$	7.20925	−	3.09748i	0.289999	−	0.124599i
$619$			35.2161i			1.41545i	0.706486	+	0.707727i	$0.250279\pi$
$619$			35.2161i			1.41545i	−0.706486	+	0.707727i	$0.749721\pi$
$620$	13.6963	+	12.9964i	0.550055	+	0.521947i
$621$	26.3825			1.05869
$622$	8.96278	+	20.8605i	0.359375	+	0.836429i
$623$	−67.2616			−2.69478
$624$	0.152292	+	2.90218i	0.00609655	+	0.116180i
$625$	−26.2641			−1.05056
$626$	−36.4934	+	15.6795i	−1.45857	+	0.626681i
$627$	12.1599	+	14.7518i	0.485620	+	0.589129i
$628$	11.6272	−	12.2534i	0.463977	−	0.488963i
$629$		−	30.7214i		−	1.22494i
$630$	−27.9659	+	12.0156i	−1.11419	+	0.478715i
$631$			1.69337i			0.0674121i	0.999432	+	0.0337061i	$0.0107310\pi$
$631$			1.69337i			0.0674121i	−0.999432	+	0.0337061i	$0.989269\pi$
$632$	6.64375	−	18.0115i	0.264274	−	0.716458i
$633$		−	12.4940i		−	0.496593i
$634$	41.4114	−	17.7926i	1.64466	−	0.706634i
$635$	2.99420			0.118821
$636$	−5.09459	−	4.83426i	−0.202014	−	0.191691i
$637$		−	7.39075i		−	0.292832i
$638$	34.6527	+	17.8475i	1.37191	+	0.706589i
$639$			6.14692i			0.243168i
$640$	24.7981	+	7.69683i	0.980232	+	0.304244i
$641$	28.0433			1.10764			0.553821	−	0.832636i	$-0.313169\pi$
$641$	28.0433			1.10764			0.553821	+	0.832636i	$0.313169\pi$
$642$	1.16936	+	2.72164i	0.0461511	+	0.107415i
$643$			27.0970i			1.06860i	0.845295	+	0.534300i	$0.179425\pi$
$643$			27.0970i			1.06860i	−0.845295	+	0.534300i	$0.820575\pi$
$644$	36.5213	+	34.6551i	1.43914	+	1.36560i
$645$			2.63364i			0.103699i
$646$	25.3010	+	58.8870i	0.995456	+	2.31688i
$647$			27.7484i			1.09090i	0.838143	+	0.545451i	$0.183642\pi$
$647$			27.7484i			1.09090i	−0.838143	+	0.545451i	$0.816358\pi$
$648$	−4.43202	+	12.0154i	−0.174106	+	0.472009i
$649$	28.6927	+	34.8084i	1.12629	+	1.36635i
$650$	0.149111	+	0.347049i	0.00584861	+	0.0136124i
$651$	11.3374			0.444347
$652$	−11.1236	−	10.5552i	−0.435635	−	0.413375i
$653$	−1.23782			−0.0484396			−0.0242198	−	0.999707i	$-0.507710\pi$
$653$	−1.23782			−0.0484396			−0.0242198	+	0.999707i	$0.507710\pi$
$654$	5.45574	−	2.34408i	0.213336	−	0.0916608i
$655$	9.61224			0.375581
$656$	−3.98608	+	0.209169i	−0.155630	+	0.00816669i
$657$		−	16.9966i		−	0.663099i
$658$	10.2429	+	23.8399i	0.399310	+	0.929376i
$659$	−46.7356			−1.82056			−0.910281	−	0.413991i	$-0.864135\pi$
$659$	−46.7356			−1.82056			−0.910281	+	0.413991i	$0.864135\pi$
$660$	−11.0335	−	0.771392i	−0.429479	−	0.0300264i
$661$	18.3173			0.712461			0.356231	−	0.934398i	$-0.384062\pi$
$661$	18.3173			0.712461			0.356231	+	0.934398i	$0.384062\pi$
$662$	−6.51387	−	15.1607i	−0.253169	−	0.589239i
$663$		−	4.15029i		−	0.161184i
$664$	−1.21289	+	3.28820i	−0.0470694	+	0.127607i
$665$	−69.0718			−2.67849
$666$	17.2753	−	7.42238i	0.669403	−	0.287611i
$667$	55.1461			2.13527
$668$	−3.58837	+	3.78160i	−0.138838	+	0.146315i
$669$	1.34243			0.0519012
$670$	2.80165	+	6.52071i	0.108237	+	0.251917i
$671$	−1.57503	−	1.91074i	−0.0608032	−	0.0737633i
$672$	13.9827	−	6.89696i	0.539394	−	0.266056i
$673$			1.38490i			0.0533839i	0.999644	+	0.0266919i	$0.00849732\pi$
$673$			1.38490i			0.0533839i	−0.999644	+	0.0266919i	$0.991503\pi$
$674$	8.17074	+	19.0170i	0.314725	+	0.732508i
$675$		−	1.06189i		−	0.0408722i
$676$	−1.37666	+	1.45079i	−0.0529485	+	0.0557998i
$677$		−	16.7270i		−	0.642872i	−0.946931	−	0.321436i	$-0.895834\pi$
$677$		−	16.7270i		−	0.642872i	0.946931	−	0.321436i	$-0.104166\pi$
$678$	3.79134	+	8.82417i	0.145605	+	0.338890i
$679$	−19.4160			−0.745119
$680$	−34.7895	−	12.8325i	−1.33411	−	0.492105i
$681$		−	8.29275i		−	0.317779i
$682$	−17.1526	−	8.83427i	−0.656809	−	0.338282i
$683$		−	11.9826i		−	0.458503i	−0.973367	−	0.229251i	$-0.926372\pi$
$683$		−	11.9826i		−	0.458503i	0.973367	−	0.229251i	$-0.0736278\pi$
$684$	−27.0005	+	28.4545i	−1.03239	+	1.08799i
$685$	23.1110			0.883025
$686$	−1.92608	+	0.827547i	−0.0735380	+	0.0315959i
$687$			3.52392i			0.134446i
$688$	0.331074	+	6.30917i	0.0126221	+	0.240535i
$689$		−	4.83328i		−	0.184133i
$690$	−14.3772	+	6.17720i	−0.547329	+	0.235162i
$691$		−	7.45353i		−	0.283546i	−0.989899	−	0.141773i	$-0.954720\pi$
$691$		−	7.45353i		−	0.283546i	0.989899	−	0.141773i	$-0.0452803\pi$
$692$	−16.6998	−	15.8465i	−0.634833	−	0.602393i
$693$	24.0007	−	19.7838i	0.911711	−	0.751525i
$694$	−37.6560	+	16.1790i	−1.42940	+	0.614147i
$695$	−30.4448			−1.15484
$696$	5.90999	−	16.0222i	0.224018	−	0.607320i
$697$	5.70034			0.215916
$698$	8.11520	+	18.8878i	0.307165	+	0.714912i
$699$	7.11878			0.269257
$700$	1.39486	−	1.46997i	0.0527207	−	0.0555598i
$701$			18.7578i			0.708472i	0.935156	+	0.354236i	$0.115259\pi$
$701$			18.7578i			0.708472i	−0.935156	+	0.354236i	$0.884741\pi$
$702$	5.16591	−	2.21955i	0.194975	−	0.0837716i
$703$	42.6675			1.60923
$704$	−26.5290	−	0.460934i	−0.999849	−	0.0173721i
$705$	−8.06456			−0.303729
$706$	44.4902	−	19.1154i	1.67441	−	0.719417i
$707$		−	36.9770i		−	1.39066i
$708$	13.6039	−	14.3365i	0.511265	−	0.538797i
$709$	39.9626			1.50083			0.750413	−	0.660969i	$-0.229854\pi$
$709$	39.9626			1.50083			0.750413	+	0.660969i	$0.229854\pi$
$710$	−3.18580	−	7.41480i	−0.119561	−	0.278272i
$711$	−16.7794			−0.629277
$712$	17.3554	−	47.0511i	0.650421	−	1.76332i
$713$	−27.2966			−1.02227
$714$	−20.4573	+	8.78958i	−0.765597	+	0.328942i
$715$	−4.84152	−	5.87348i	−0.181063	−	0.219656i
$716$	−8.75943	−	8.31183i	−0.327355	−	0.310628i
$717$		−	12.5392i		−	0.468285i
$718$	26.9198	−	11.5662i	1.00464	−	0.431647i
$719$		−	25.4562i		−	0.949356i	−0.880159	−	0.474678i	$-0.842564\pi$
$719$		−	25.4562i		−	0.949356i	0.880159	−	0.474678i	$-0.157436\pi$
$720$	−1.18925	−	22.6632i	−0.0443207	−	0.844607i
$721$		−	28.9696i		−	1.07888i
$722$	−57.0975	+	24.5322i	−2.12495	+	0.912992i
$723$	−6.15157			−0.228779
$724$	−25.9913	+	27.3909i	−0.965959	+	1.01798i
$725$		−	2.21962i		−	0.0824346i
$726$	11.0451	−	2.39784i	0.409921	−	0.0889924i
$727$		−	18.4946i		−	0.685928i	−0.939349	−	0.342964i	$-0.888569\pi$
$727$		−	18.4946i		−	0.685928i	0.939349	−	0.342964i	$-0.111431\pi$
$728$	10.0667	+	3.71322i	0.373096	+	0.137621i
$729$	2.52786			0.0936244
$730$	8.80889	+	20.5023i	0.326032	+	0.758824i
$731$		−	9.02250i		−	0.333709i
$732$	−0.746758	+	0.786971i	−0.0276010	+	0.0290873i
$733$		−	5.66328i		−	0.209178i	−0.994516	−	0.104589i	$-0.966647\pi$
$733$		−	5.66328i		−	0.209178i	0.994516	−	0.104589i	$-0.0333527\pi$
$734$	−11.4464	−	26.6410i	−0.422495	−	0.983338i
$735$		−	12.3235i		−	0.454560i
$736$	−33.6656	+	16.6055i	−1.24093	+	0.612088i
$737$	−4.61293	−	5.59616i	−0.169919	−	0.206137i
$738$	1.37722	+	3.20541i	0.0506961	+	0.117993i
$739$	−4.09154			−0.150510			−0.0752549	−	0.997164i	$-0.523977\pi$
$739$	−4.09154			−0.150510			−0.0752549	+	0.997164i	$0.523977\pi$
$740$	−16.9917	+	17.9067i	−0.624626	+	0.658263i
$741$	5.76414			0.211751
$742$	−23.8239	+	10.2360i	−0.874602	+	0.375776i
$743$	34.9224			1.28118			0.640589	−	0.767884i	$-0.278690\pi$
$743$	34.9224			1.28118			0.640589	+	0.767884i	$0.278690\pi$
$744$	−2.92537	+	7.93078i	−0.107249	+	0.290756i
$745$			45.1652i			1.65473i
$746$	−3.27639	−	7.62566i	−0.119957	−	0.279195i
$747$	3.06328			0.112079
$748$	37.7994	+	2.64269i	1.38208	+	0.0966263i
$749$	10.9366			0.399616
$750$	−4.40577	−	10.2542i	−0.160876	−	0.374432i
$751$			12.4644i			0.454831i	0.973798	+	0.227416i	$0.0730276\pi$
$751$			12.4644i			0.454831i	−0.973798	+	0.227416i	$0.926972\pi$
$752$	−19.3195	+	1.01379i	−0.704511	+	0.0369692i
$753$	−9.57648			−0.348986
$754$	10.7981	−	4.63942i	0.393242	−	0.168958i
$755$	−12.9050			−0.469660
$756$	−21.8809	−	20.7628i	−0.795802	−	0.755137i
$757$	24.2774			0.882375			0.441188	−	0.897415i	$-0.354557\pi$
$757$	24.2774			0.882375			0.441188	+	0.897415i	$0.354557\pi$
$758$	18.4406	+	42.9196i	0.669792	+	1.55891i
$759$	12.3387	−	10.1708i	0.447866	−	0.369177i
$760$	17.8225	−	48.3174i	0.646488	−	1.75265i
$761$			13.5039i			0.489517i	0.969584	+	0.244759i	$0.0787087\pi$
$761$			13.5039i			0.489517i	−0.969584	+	0.244759i	$0.921291\pi$
$762$	0.529180	+	1.23164i	0.0191702	+	0.0446177i
$763$		−	21.9233i		−	0.793676i
$764$	−29.9946	−	28.4619i	−1.08517	−	1.02972i
$765$			32.4097i			1.17178i
$766$	−13.5683	−	31.5797i	−0.490244	−	1.14102i
$767$	13.6011			0.491108
$768$	1.21666	+	11.5608i	0.0439025	+	0.417166i
$769$		−	2.96166i		−	0.106800i	−0.998573	−	0.0534000i	$-0.982994\pi$
$769$		−	2.96166i		−	0.106800i	0.998573	−	0.0534000i	$-0.0170058\pi$
$770$	−18.6977	+	36.3035i	−0.673817	+	1.30829i
$771$			4.13454i			0.148902i
$772$	10.2189	+	9.69671i	0.367786	+	0.348992i
$773$	3.68789			0.132644			0.0663220	−	0.997798i	$-0.478874\pi$
$773$	3.68789			0.132644			0.0663220	+	0.997798i	$0.478874\pi$
$774$	5.07353	−	2.17986i	0.182364	−	0.0783535i
$775$			1.09868i			0.0394658i
$776$	5.00989	−	13.5820i	0.179844	−	0.487565i
$777$			14.8227i			0.531760i
$778$	−21.1666	+	9.09433i	−0.758861	+	0.326047i
$779$			7.91692i			0.283653i
$780$	−2.29548	+	2.41909i	−0.0821914	+	0.0866174i
$781$	5.24543	+	6.36348i	0.187696	+	0.227703i
$782$	49.2543	−	21.1623i	1.76133	−	0.756763i
$783$	−33.0396			−1.18074
$784$	−1.54919	−	29.5224i	−0.0553281	−	1.05437i
$785$	19.3836			0.691831
$786$	1.69882	+	3.95393i	0.0605949	+	0.141032i
$787$	27.4844			0.979714			0.489857	−	0.871803i	$-0.337049\pi$
$787$	27.4844			0.979714			0.489857	+	0.871803i	$0.337049\pi$
$788$	34.0048	+	32.2672i	1.21137	+	1.14947i
$789$			7.03286i			0.250376i
$790$	20.2404	−	8.69636i	0.720120	−	0.309402i
$791$	35.4589			1.26077
$792$	7.64641	+	21.8938i	0.271703	+	0.777964i
$793$	−0.746606			−0.0265128
$794$	−8.06761	+	3.46628i	−0.286309	+	0.123014i
$795$		−	8.05914i		−	0.285828i
$796$	32.2108	+	30.5648i	1.14168	+	1.08334i
$797$	−37.9719			−1.34503			−0.672517	−	0.740082i	$-0.734787\pi$
$797$	−37.9719			−1.34503			−0.672517	+	0.740082i	$0.734787\pi$
$798$	−12.2074	−	28.4122i	−0.432138	−	1.00578i
$799$	27.6282			0.977414
$800$	0.668369	+	1.35503i	0.0236304	+	0.0479076i
$801$	−43.8327			−1.54875
$802$	−12.2847	+	5.27817i	−0.433788	+	0.186379i
$803$	−14.5039	−	17.5954i	−0.511831	−	0.620927i
$804$	−2.18710	+	2.30488i	−0.0771331	+	0.0812867i
$805$			57.7731i			2.03623i
$806$	−5.34489	+	2.29645i	−0.188266	+	0.0808891i
$807$		−	7.51077i		−	0.264392i
$808$	25.8663	+	9.54111i	0.909974	+	0.335655i
$809$			29.4596i			1.03574i	0.855458	+	0.517872i	$0.173276\pi$
$809$			29.4596i			1.03574i	−0.855458	+	0.517872i	$0.826724\pi$
$810$	−13.5023	+	5.80131i	−0.474422	+	0.203837i
$811$	−26.0802			−0.915800			−0.457900	−	0.889004i	$-0.651398\pi$
$811$	−26.0802			−0.915800			−0.457900	+	0.889004i	$0.651398\pi$
$812$	−45.7367	−	43.3996i	−1.60504	−	1.52303i
$813$		−	7.62847i		−	0.267542i
$814$	11.5500	−	22.4256i	0.404829	−	0.786017i
$815$		−	17.5965i		−	0.616379i
$816$	−0.869950	−	16.5784i	−0.0304543	−	0.580359i
$817$	12.5309			0.438401
$818$	−1.90946	−	4.44419i	−0.0667628	−	0.155387i
$819$		−	9.37808i		−	0.327697i
$820$	−3.32257	−	3.15279i	−0.116029	−	0.110100i
$821$		−	20.5575i		−	0.717462i	−0.933441	−	0.358731i	$-0.883210\pi$
$821$		−	20.5575i		−	0.717462i	0.933441	−	0.358731i	$-0.116790\pi$
$822$	4.08452	+	9.50654i	0.142464	+	0.331579i
$823$		−	15.8354i		−	0.551987i	−0.961159	−	0.275994i	$-0.910993\pi$
$823$		−	15.8354i		−	0.551987i	0.961159	−	0.275994i	$-0.0890069\pi$
$824$	20.2649	+	7.47496i	0.705962	+	0.260403i
$825$	−0.409373	−	0.496630i	−0.0142525	−	0.0172904i
$826$	−28.8047	−	67.0417i	−1.00224	−	2.33268i
$827$	−27.9287			−0.971176			−0.485588	−	0.874188i	$-0.661395\pi$
$827$	−27.9287			−0.971176			−0.485588	+	0.874188i	$0.661395\pi$
$828$	23.8000	+	22.5838i	0.827106	+	0.784842i
$829$	34.2424			1.18929			0.594644	−	0.803989i	$-0.297293\pi$
$829$	34.2424			1.18929			0.594644	+	0.803989i	$0.297293\pi$
$830$	−3.69512	+	1.58762i	−0.128259	+	0.0551071i
$831$	13.6036			0.471905
$832$	−5.19497	+	6.08377i	−0.180103	+	0.210917i
$833$			42.2189i			1.46280i
$834$	−5.38067	−	12.5233i	−0.186317	−	0.433646i
$835$	−5.98213			−0.207020
$836$	−3.67030	+	52.4978i	−0.126940	+	1.81567i
$837$	16.3542			0.565283
$838$	−4.69356	−	10.9241i	−0.162136	−	0.377365i
$839$		−	6.90054i		−	0.238233i	−0.992880	−	0.119117i	$-0.961994\pi$
$839$		−	6.90054i		−	0.238233i	0.992880	−	0.119117i	$-0.0380062\pi$
$840$	16.7854	+	6.19152i	0.579153	+	0.213628i
$841$	−40.0611			−1.38142
$842$	47.5995	−	20.4513i	1.64039	−	0.704798i
$843$	4.96715			0.171078
$844$	23.6738	−	24.9487i	0.814887	−	0.858769i
$845$	−2.29501			−0.0789509
$846$	6.67504	+	15.5359i	0.229493	+	0.534134i
$847$	7.96386	−	40.9617i	0.273642	−	1.40746i
$848$	−1.01311	−	19.3066i	−0.0347904	−	0.662990i
$849$		−	2.35102i		−	0.0806869i
$850$	−0.851779	−	1.98248i	−0.0292158	−	0.0679984i
$851$		−	35.6880i		−	1.22337i
$852$	2.48698	−	2.62091i	0.0852027	−	0.0897909i
$853$			25.7011i			0.879989i	0.898000	+	0.439995i	$0.145020\pi$
$853$			25.7011i			0.879989i	−0.898000	+	0.439995i	$0.854980\pi$
$854$	1.58118	+	3.68012i	0.0541068	+	0.125931i
$855$	−45.0123			−1.53939
$856$	−2.82196	+	7.65043i	−0.0964525	+	0.261486i
$857$		−	32.7134i		−	1.11747i	−0.829347	−	0.558734i	$-0.811287\pi$
$857$		−	32.7134i		−	1.11747i	0.829347	−	0.558734i	$-0.188713\pi$
$858$	1.56035	−	3.02958i	0.0532694	−	0.103428i
$859$			26.5501i			0.905877i	0.891542	+	0.452939i	$0.149624\pi$
$859$			26.5501i			0.905877i	−0.891542	+	0.452939i	$0.850376\pi$
$860$	−4.99024	+	5.25897i	−0.170166	+	0.179329i
$861$	−2.75034			−0.0937312
$862$	−22.7593	+	9.77862i	−0.775185	+	0.333061i
$863$		−	32.5393i		−	1.10765i	−0.832633	−	0.553825i	$-0.813168\pi$
$863$		−	32.5393i		−	1.10765i	0.832633	−	0.553825i	$-0.186832\pi$
$864$	20.1700	−	9.94884i	0.686197	−	0.338467i
$865$		−	26.4175i		−	0.898222i
$866$	1.20845	−	0.519215i	0.0410648	−	0.0176436i
$867$			11.3569i			0.385699i
$868$	22.6390	+	21.4822i	0.768419	+	0.729154i
$869$	−17.3706	+	14.3186i	−0.589256	+	0.485725i
$870$	18.0050	−	7.73590i	0.610425	−	0.262271i
$871$	−2.18666			−0.0740920
$872$	15.3359	+	5.65683i	0.519338	+	0.191564i
$873$	−12.6529			−0.428237
$874$	29.3913	+	68.4069i	0.994175	+	2.31390i
$875$	−41.2055			−1.39300
$876$	−6.87664	+	7.24696i	−0.232340	+	0.244852i
$877$			4.24231i			0.143253i	0.997432	+	0.0716263i	$0.0228189\pi$
$877$			4.24231i			0.143253i	−0.997432	+	0.0716263i	$0.977181\pi$
$878$	19.1897	−	8.24492i	0.647621	−	0.278253i
$879$	21.3526			0.720206
$880$	−20.5706	−	22.4468i	−0.693435	−	0.756681i
$881$	37.8100			1.27385			0.636926	−	0.770925i	$-0.280206\pi$
$881$	37.8100			1.27385			0.636926	+	0.770925i	$0.280206\pi$
$882$	−23.7405	+	10.2002i	−0.799384	+	0.343458i
$883$			44.4667i			1.49642i	0.663460	+	0.748212i	$0.269087\pi$
$883$			44.4667i			1.49642i	−0.663460	+	0.748212i	$0.730913\pi$
$884$	7.86402	−	8.28750i	0.264496	−	0.278739i
$885$	22.6789			0.762342
$886$	3.66686	+	8.53445i	0.123191	+	0.286720i
$887$	−11.6285			−0.390448			−0.195224	−	0.980759i	$-0.562543\pi$
$887$	−11.6285			−0.390448			−0.195224	+	0.980759i	$0.562543\pi$
$888$	−10.3688	−	3.82467i	−0.347955	−	0.128347i
$889$	4.94922			0.165992
$890$	52.8737	−	22.7174i	1.77233	−	0.761489i
$891$	11.5879	−	9.55189i	0.388208	−	0.320000i
$892$	2.68062	+	2.54364i	0.0897538	+	0.0851675i
$893$			38.3714i			1.28405i
$894$	−18.5784	+	7.98229i	−0.621355	+	0.266968i
$895$		−	13.8565i		−	0.463173i
$896$	40.9897	+	12.7224i	1.36937	+	0.425025i
$897$		−	4.82124i		−	0.160977i
$898$	43.8734	−	18.8504i	1.46407	−	0.629045i
$899$	34.1843			1.14011
$900$	0.908994	−	0.957944i	0.0302998	−	0.0319315i
$901$			27.6096i			0.919809i
$902$	4.16106	+	2.14310i	0.138548	+	0.0713575i
$903$			4.35323i			0.144867i
$904$	−9.14940	+	24.8044i	−0.304305	+	0.824981i
$905$	−43.3298			−1.44033
$906$	−2.28076	−	5.30837i	−0.0757732	−	0.176359i
$907$		−	40.6776i		−	1.35068i	−0.737507	−	0.675339i	$-0.763997\pi$
$907$		−	40.6776i		−	1.35068i	0.737507	−	0.675339i	$-0.236003\pi$
$908$	15.7132	−	16.5594i	0.521461	−	0.549542i
$909$		−	24.0970i		−	0.799246i
$910$	4.86043	+	11.3124i	0.161122	+	0.375003i
$911$			25.1795i			0.834235i	0.908853	+	0.417117i	$0.136960\pi$
$911$			25.1795i			0.834235i	−0.908853	+	0.417117i	$0.863040\pi$
$912$	23.0249	−	1.20823i	0.762430	−	0.0400085i
$913$	3.17120	−	2.61403i	0.104951	−	0.0865117i
$914$	22.9355	+	53.3813i	0.758638	+	1.76570i
$915$	−1.24491			−0.0411555
$916$	−6.67715	+	7.03672i	−0.220619	+	0.232500i
$917$	15.8884			0.524682
$918$	−29.5097	+	12.6789i	−0.973964	+	0.418467i
$919$	−0.610024			−0.0201228			−0.0100614	−	0.999949i	$-0.503203\pi$
$919$	−0.610024			−0.0201228			−0.0100614	+	0.999949i	$0.503203\pi$
$920$	−40.4136	−	14.9071i	−1.33240	−	0.491472i
$921$		−	4.11107i		−	0.135464i
$922$	−20.8233	−	48.4654i	−0.685780	−	1.59612i
$923$	2.48648			0.0818435
$924$	−18.2377	−	1.27506i	−0.599977	−	0.0419465i
$925$	−1.43643			−0.0472296
$926$	−7.83811	−	18.2429i	−0.257576	−	0.599497i
$927$		−	18.8787i		−	0.620059i
$928$	42.1604	−	20.7956i	1.38398	−	0.682649i
$929$	−2.17142			−0.0712419			−0.0356210	−	0.999365i	$-0.511341\pi$
$929$	−2.17142			−0.0712419			−0.0356210	+	0.999365i	$0.511341\pi$
$930$	−8.91221	+	3.82917i	−0.292243	+	0.125563i
$931$	−58.6357			−1.92171
$932$	14.2151	+	13.4887i	0.465632	+	0.441838i
$933$	−11.6642			−0.381870
$934$	1.38468	+	3.22277i	0.0453080	+	0.105452i
$935$	27.6566	+	33.5516i	0.904469	+	1.09725i
$936$	6.56020	+	2.41981i	0.214427	+	0.0790939i
$937$			33.5328i			1.09547i	0.836653	+	0.547734i	$0.184509\pi$
$937$			33.5328i			1.09547i	−0.836653	+	0.547734i	$0.815491\pi$
$938$	4.63095	+	10.7783i	0.151206	+	0.351925i
$939$		−	20.4055i		−	0.665908i
$940$	−16.1037	−	15.2808i	−0.525245	−	0.498405i
$941$		−	23.0472i		−	0.751318i	−0.926758	−	0.375659i	$-0.877416\pi$
$941$		−	23.0472i		−	0.751318i	0.926758	−	0.375659i	$-0.122584\pi$
$942$	3.42577	+	7.97332i	0.111618	+	0.259785i
$943$	6.62187			0.215638
$944$	54.3297	−	2.85095i	1.76828	−	0.0927906i
$945$		−	34.6135i		−	1.12598i
$946$	3.39211	−	6.58612i	0.110287	−	0.214133i
$947$			0.648606i			0.0210769i	0.999944	+	0.0105384i	$0.00335455\pi$
$947$			0.648606i			0.0210769i	−0.999944	+	0.0105384i	$0.996645\pi$
$948$	7.15437	+	6.78879i	0.232363	+	0.220490i
$949$	−6.87525			−0.223180
$950$	2.75337	−	1.18299i	0.0893310	−	0.0383814i
$951$			23.1554i			0.750866i
$952$	−57.5048	−	21.2114i	−1.86374	−	0.687464i
$953$			2.47723i			0.0802452i	0.999195	+	0.0401226i	$0.0127749\pi$
$953$			2.47723i			0.0802452i	−0.999195	+	0.0401226i	$0.987225\pi$
$954$	−15.5254	+	6.67055i	−0.502654	+	0.215967i
$955$		−	47.4485i		−	1.53540i
$956$	23.7594	−	25.0389i	0.768434	−	0.809814i
$957$	−15.4521	+	12.7372i	−0.499495	+	0.411735i
$958$	36.5224	−	15.6920i	1.17999	−	0.506986i
$959$	38.2010			1.23357
$960$	−8.66223	+	10.1442i	−0.279572	+	0.327404i
$961$	14.0792			0.454168
$962$	−3.00242	−	6.98799i	−0.0968018	−	0.225302i
$963$	7.12712			0.229668
$964$	−12.2838	−	11.6561i	−0.395633	−	0.375416i
$965$			16.1653i			0.520379i
$966$	−23.7646	+	10.2105i	−0.764612	+	0.328518i
$967$	−24.8345			−0.798624			−0.399312	−	0.916815i	$-0.630751\pi$
$967$	−24.8345			−0.798624			−0.399312	+	0.916815i	$0.630751\pi$
$968$	26.5988	+	16.1402i	0.854917	+	0.518765i
$969$	−32.9270			−1.05777
$970$	15.2628	−	6.55770i	0.490058	−	0.210555i
$971$			5.56158i			0.178480i	0.996010	+	0.0892398i	$0.0284437\pi$
$971$			5.56158i			0.178480i	−0.996010	+	0.0892398i	$0.971556\pi$
$972$	−22.0766	−	20.9485i	−0.708108	−	0.671924i
$973$	−50.3234			−1.61329
$974$	−15.7360	−	36.6249i	−0.504214	−	1.17354i
$975$	−0.194054			−0.00621471
$976$	−2.98232	+	0.156497i	−0.0954618	+	0.00500936i
$977$	52.8402			1.69051			0.845253	−	0.534366i	$-0.179450\pi$
$977$	52.8402			1.69051			0.845253	+	0.534366i	$0.179450\pi$
$978$	7.23820	−	3.10992i	0.231452	−	0.0994443i
$979$	−45.3770	+	37.4043i	−1.45025	+	1.19545i
$980$	23.3508	−	24.6082i	0.745913	−	0.786081i
$981$		−	14.2868i		−	0.456144i
$982$	5.45595	−	2.34417i	0.174106	−	0.0748055i
$983$			21.7483i			0.693663i	0.937927	+	0.346831i	$0.112742\pi$
$983$			21.7483i			0.693663i	−0.937927	+	0.346831i	$0.887258\pi$
$984$	0.709664	−	1.92393i	0.0226233	−	0.0613325i
$985$			53.7923i			1.71396i
$986$	−61.6827	+	26.5022i	−1.96438	+	0.844002i
$987$	−13.3302			−0.424305
$988$	11.5101	+	10.9219i	0.366185	+	0.347473i
$989$		−	10.4811i		−	0.333280i
$990$	−12.1848	+	23.6580i	−0.387258	+	0.751901i
$991$		−	59.2302i		−	1.88151i	−0.339089	−	0.940754i	$-0.610119\pi$
$991$		−	59.2302i		−	1.88151i	0.339089	−	0.940754i	$-0.389881\pi$
$992$	−20.8688	+	10.2935i	−0.662586	+	0.326820i
$993$	8.47721			0.269016
$994$	−5.26592	−	12.2562i	−0.167025	−	0.388743i
$995$			50.9543i			1.61536i
$996$	−1.30611	−	1.23937i	−0.0413858	−	0.0392710i
$997$			21.6005i			0.684094i	0.939683	+	0.342047i	$0.111120\pi$
$997$			21.6005i			0.684094i	−0.939683	+	0.342047i	$0.888880\pi$
$998$	22.4837	+	52.3298i	0.711710	+	1.65647i
$999$			21.3817i			0.676486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.10	yes	64
4.3	odd	2	inner	572.2.e.b.131.56	yes	64
11.10	odd	2	inner	572.2.e.b.131.55	yes	64
44.43	even	2	inner	572.2.e.b.131.9	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.9	✓	64	44.43	even	2	inner
572.2.e.b.131.10	yes	64	1.1	even	1	trivial
572.2.e.b.131.55	yes	64	11.10	odd	2	inner
572.2.e.b.131.56	yes	64	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29936 + 0.558274i) q^{2} -0.726543i q^{3} +(1.37666 - 1.45079i) q^{4} +2.29501 q^{5} +(0.405610 + 0.944039i) q^{6} +3.79351 q^{7} +(-0.978833 + 2.65366i) q^{8} +2.47214 q^{9} +O(q^{10})\)	\(q+(-1.29936 + 0.558274i) q^{2} -0.726543i q^{3} +(1.37666 - 1.45079i) q^{4} +2.29501 q^{5} +(0.405610 + 0.944039i) q^{6} +3.79351 q^{7} +(-0.978833 + 2.65366i) q^{8} +2.47214 q^{9} +(-2.98204 + 1.28125i) q^{10} +(2.55923 - 2.10958i) q^{11} +(-1.05406 - 1.00020i) q^{12} -1.00000i q^{13} +(-4.92913 + 2.11782i) q^{14} -1.66743i q^{15} +(-0.209612 - 3.99450i) q^{16} +5.71239i q^{17} +(-3.21219 + 1.38013i) q^{18} -7.93365 q^{19} +(3.15946 - 3.32960i) q^{20} -2.75615i q^{21} +(-2.14763 + 4.16985i) q^{22} +6.63587i q^{23} +(1.92799 + 0.711164i) q^{24} +0.267093 q^{25} +(0.558274 + 1.29936i) q^{26} -3.97574i q^{27} +(5.22238 - 5.50361i) q^{28} -8.31030i q^{29} +(0.930880 + 2.16658i) q^{30} +4.11349i q^{31} +(2.50239 + 5.07327i) q^{32} +(-1.53270 - 1.85939i) q^{33} +(-3.18908 - 7.42244i) q^{34} +8.70617 q^{35} +(3.40329 - 3.58656i) q^{36} -5.37803 q^{37} +(10.3087 - 4.42915i) q^{38} -0.726543 q^{39} +(-2.24644 + 6.09018i) q^{40} -0.997890i q^{41} +(1.53869 + 3.58122i) q^{42} -1.57946 q^{43} +(0.462624 - 6.61710i) q^{44} +5.67359 q^{45} +(-3.70463 - 8.62237i) q^{46} -4.83653i q^{47} +(-2.90218 + 0.152292i) q^{48} +7.39075 q^{49} +(-0.347049 + 0.149111i) q^{50} +4.15029 q^{51} +(-1.45079 - 1.37666i) q^{52} +4.83328 q^{53} +(2.21955 + 5.16591i) q^{54} +(5.87348 - 4.84152i) q^{55} +(-3.71322 + 10.0667i) q^{56} +5.76414i q^{57} +(4.63942 + 10.7981i) q^{58} +13.6011i q^{59} +(-2.41909 - 2.29548i) q^{60} -0.746606i q^{61} +(-2.29645 - 5.34489i) q^{62} +9.37808 q^{63} +(-6.08377 - 5.19497i) q^{64} -2.29501i q^{65} +(3.02958 + 1.56035i) q^{66} -2.18666i q^{67} +(8.28750 + 7.86402i) q^{68} +4.82124 q^{69} +(-11.3124 + 4.86043i) q^{70} +2.48648i q^{71} +(-2.41981 + 6.56020i) q^{72} -6.87525i q^{73} +(6.98799 - 3.00242i) q^{74} -0.194054i q^{75} +(-10.9219 + 11.5101i) q^{76} +(9.70848 - 8.00273i) q^{77} +(0.944039 - 0.405610i) q^{78} -6.78742 q^{79} +(-0.481062 - 9.16745i) q^{80} +4.52786 q^{81} +(0.557096 + 1.29662i) q^{82} +1.23912 q^{83} +(-3.99861 - 3.79428i) q^{84} +13.1100i q^{85} +(2.05229 - 0.881772i) q^{86} -6.03779 q^{87} +(3.09304 + 8.85625i) q^{88} -17.7307 q^{89} +(-7.37202 + 3.16742i) q^{90} -3.79351i q^{91} +(9.62729 + 9.13534i) q^{92} +2.98862 q^{93} +(2.70011 + 6.28438i) q^{94} -18.2079 q^{95} +(3.68595 - 1.81809i) q^{96} -5.11822 q^{97} +(-9.60323 + 4.12607i) q^{98} +(6.32677 - 5.21517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

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Database

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