LMFDB - Embedded newform 507.2.t.a.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

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

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			10.4
Character	$\chi$	$=$	507.10
Dual form			507.2.t.a.355.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78276 - 0.363953i) q^{2} +(0.987050 - 0.160411i) q^{3} +(1.20581 + 0.513748i) q^{4} +(0.718046 - 2.91323i) q^{5} +(-1.81806 - 0.0732651i) q^{6} +(-2.45740 + 1.16605i) q^{7} +(1.03220 + 0.712476i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})$	\(q+(-1.78276 - 0.363953i) q^{2} +(0.987050 - 0.160411i) q^{3} +(1.20581 + 0.513748i) q^{4} +(0.718046 - 2.91323i) q^{5} +(-1.81806 - 0.0732651i) q^{6} +(-2.45740 + 1.16605i) q^{7} +(1.03220 + 0.712476i) q^{8} +(0.948536 - 0.316668i) q^{9} +(-2.34038 + 4.93225i) q^{10} +(0.727030 - 2.17772i) q^{11} +(1.27261 + 0.313669i) q^{12} +(-1.22410 - 3.39140i) q^{13} +(4.80535 - 1.18441i) q^{14} +(0.241433 - 2.99068i) q^{15} +(-3.39675 - 3.53639i) q^{16} +(0.309247 + 0.651725i) q^{17} +(-1.80626 + 0.219320i) q^{18} +(-1.49069 - 0.860650i) q^{19} +(2.36249 - 3.14390i) q^{20} +(-2.23853 + 1.54515i) q^{21} +(-2.08871 + 3.61775i) q^{22} +(0.320417 + 0.554979i) q^{23} +(1.13312 + 0.537673i) q^{24} +(-3.54401 - 1.86004i) q^{25} +(0.947964 + 6.49156i) q^{26} +(0.885456 - 0.464723i) q^{27} +(-3.56222 + 0.143552i) q^{28} +(-0.791728 + 3.87814i) q^{29} +(-1.51888 + 5.24380i) q^{30} +(-3.55260 - 6.76892i) q^{31} +(3.42784 + 5.42070i) q^{32} +(0.368284 - 2.26614i) q^{33} +(-0.314116 - 1.27442i) q^{34} +(1.63245 + 7.99625i) q^{35} +(1.30644 + 0.105467i) q^{36} +(-0.705363 + 1.11544i) q^{37} +(2.34431 + 2.07687i) q^{38} +(-1.75227 - 3.15112i) q^{39} +(2.81677 - 2.49544i) q^{40} +(-1.47321 - 9.06503i) q^{41} +(4.55313 - 1.93991i) q^{42} +(-7.84941 + 4.96367i) q^{43} +(1.99546 - 2.25241i) q^{44} +(-0.241433 - 2.99068i) q^{45} +(-0.369241 - 1.10601i) q^{46} +(-0.787002 - 0.0955593i) q^{47} +(-3.92004 - 2.94572i) q^{48} +(0.252034 - 0.308686i) q^{49} +(5.64116 + 4.60586i) q^{50} +(0.409786 + 0.593678i) q^{51} +(0.266293 - 4.71826i) q^{52} +(7.31357 - 10.5955i) q^{53} +(-1.74769 + 0.506225i) q^{54} +(-5.82215 - 3.68170i) q^{55} +(-3.36732 - 0.547242i) q^{56} +(-1.60944 - 0.610382i) q^{57} +(2.82292 - 6.62563i) q^{58} +(-6.27807 - 6.03017i) q^{59} +(1.82758 - 3.48216i) q^{60} +(-4.52213 + 0.365064i) q^{61} +(3.86987 + 13.3603i) q^{62} +(-1.96168 + 1.88422i) q^{63} +(-0.660547 - 1.74172i) q^{64} +(-10.7589 + 1.13090i) q^{65} +(-1.48133 + 3.90595i) q^{66} +(0.135153 + 0.317215i) q^{67} +(0.0380714 + 0.944731i) q^{68} +(0.405293 + 0.496394i) q^{69} -14.8495i q^{70} +(-1.91642 + 1.56471i) q^{71} +(1.20470 + 0.348945i) q^{72} +(-3.27141 - 3.69266i) q^{73} +(1.66346 - 1.73185i) q^{74} +(-3.79649 - 1.26746i) q^{75} +(-1.35533 - 1.80362i) q^{76} +(0.752730 + 6.19929i) q^{77} +(1.97701 + 6.25543i) q^{78} +(-0.845391 + 6.96242i) q^{79} +(-12.7413 + 7.35622i) q^{80} +(0.799443 - 0.600742i) q^{81} +(-0.672864 + 16.6969i) q^{82} +(-2.53465 + 0.961265i) q^{83} +(-3.49306 + 0.713113i) q^{84} +(2.12067 - 0.432939i) q^{85} +(15.8001 - 5.99221i) q^{86} +(-0.159378 + 3.95492i) q^{87} +(2.30201 - 1.72985i) q^{88} +(10.5060 - 6.06567i) q^{89} +(-0.658051 + 5.41954i) q^{90} +(6.96265 + 6.90667i) q^{91} +(0.101243 + 0.833813i) q^{92} +(-4.59241 - 6.11139i) q^{93} +(1.36826 + 0.456791i) q^{94} +(-3.57765 + 3.72473i) q^{95} +(4.25299 + 4.80063i) q^{96} +(12.1748 + 3.52648i) q^{97} +(-0.561663 + 0.458584i) q^{98} -2.29587i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{78}\right)$

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 $

$2$	−1.78276	−	0.363953i	−1.26060	−	0.257354i	−0.477158	−	0.878817i	$-0.658333\pi$
$2$	−1.78276	−	0.363953i	−1.26060	−	0.257354i	−0.783443	+	0.621464i	$0.786538\pi$
$3$	0.987050	−	0.160411i	0.569874	−	0.0926135i
$3$	0.987050	−	0.160411i	0.569874	−	0.0926135i
$4$	1.20581	+	0.513748i	0.602905	+	0.256874i
$5$	0.718046	−	2.91323i	0.321120	−	1.30283i	−0.559429	−	0.828878i	$-0.688979\pi$
$5$	0.718046	−	2.91323i	0.321120	−	1.30283i	0.880549	−	0.473956i	$-0.157174\pi$
$6$	−1.81806	−	0.0732651i	−0.742218	−	0.0299104i
$7$	−2.45740	+	1.16605i	−0.928811	+	0.440726i	−0.832125	−	0.554589i	$-0.812876\pi$
$7$	−2.45740	+	1.16605i	−0.928811	+	0.440726i	−0.0966863	+	0.995315i	$0.530824\pi$
$8$	1.03220	+	0.712476i	0.364938	+	0.251898i
$9$	0.948536	−	0.316668i	0.316179	−	0.105556i
$10$	−2.34038	+	4.93225i	−0.740093	+	1.55971i
$11$	0.727030	−	2.17772i	0.219208	−	0.656607i	−0.780305	−	0.625399i	$-0.784936\pi$
$11$	0.727030	−	2.17772i	0.219208	−	0.656607i	0.999513	−	0.0312084i	$-0.00993555\pi$
$12$	1.27261	+	0.313669i	0.367370	+	0.0905485i
$13$	−1.22410	−	3.39140i	−0.339504	−	0.940605i
$13$	−1.22410	−	3.39140i	−0.339504	−	0.940605i
$14$	4.80535	−	1.18441i	1.28428	−	0.316547i
$15$	0.241433	−	2.99068i	0.0623377	−	0.772191i
$16$	−3.39675	−	3.53639i	−0.849188	−	0.884099i
$17$	0.309247	+	0.651725i	0.0750035	+	0.158066i	0.937489	−	0.348016i	$-0.113144\pi$
$17$	0.309247	+	0.651725i	0.0750035	+	0.158066i	−0.862485	+	0.506082i	$0.831093\pi$
$18$	−1.80626	+	0.219320i	−0.425741	+	0.0516943i
$19$	−1.49069	−	0.860650i	−0.341988	−	0.197447i	0.319163	−	0.947700i	$-0.396598\pi$
$19$	−1.49069	−	0.860650i	−0.341988	−	0.197447i	−0.661151	+	0.750253i	$0.729932\pi$
$20$	2.36249	−	3.14390i	0.528269	−	0.702998i
$21$	−2.23853	+	1.54515i	−0.488488	+	0.337179i
$22$	−2.08871	+	3.61775i	−0.445314	+	0.771306i
$23$	0.320417	+	0.554979i	0.0668116	+	0.115721i	0.897496	−	0.441022i	$-0.145384\pi$
$23$	0.320417	+	0.554979i	0.0668116	+	0.115721i	−0.830685	+	0.556743i	$0.812051\pi$
$24$	1.13312	+	0.537673i	0.231298	+	0.109752i
$25$	−3.54401	−	1.86004i	−0.708803	−	0.372008i
$26$	0.947964	+	6.49156i	0.185911	+	1.27310i
$27$	0.885456	−	0.464723i	0.170406	−	0.0894360i
$28$	−3.56222	+	0.143552i	−0.673196	+	0.0271289i
$29$	−0.791728	+	3.87814i	−0.147020	+	0.720152i	0.837717	+	0.546104i	$0.183890\pi$
$29$	−0.791728	+	3.87814i	−0.147020	+	0.720152i	−0.984737	+	0.174048i	$0.944315\pi$
$30$	−1.51888	+	5.24380i	−0.277309	+	0.957382i
$31$	−3.55260	−	6.76892i	−0.638067	−	1.21573i	−0.962873	−	0.269954i	$-0.912992\pi$
$31$	−3.55260	−	6.76892i	−0.638067	−	1.21573i	0.324807	−	0.945780i	$-0.394701\pi$
$32$	3.42784	+	5.42070i	0.605962	+	0.958253i
$33$	0.368284	−	2.26614i	0.0641100	−	0.394485i
$34$	−0.314116	−	1.27442i	−0.0538705	−	0.218561i
$35$	1.63245	+	7.99625i	0.275934	+	1.35161i
$36$	1.30644	+	0.105467i	0.217740	+	0.0175778i
$37$	−0.705363	+	1.11544i	−0.115961	+	0.183378i	−0.898183	−	0.439623i	$-0.855112\pi$
$37$	−0.705363	+	1.11544i	−0.115961	+	0.183378i	0.782222	+	0.623000i	$0.214087\pi$
$38$	2.34431	+	2.07687i	0.380297	+	0.336913i
$39$	−1.75227	−	3.15112i	−0.280587	−	0.504583i
$40$	2.81677	−	2.49544i	0.445371	−	0.394564i
$41$	−1.47321	−	9.06503i	−0.230077	−	1.41572i	−0.802936	−	0.596066i	$-0.796730\pi$
$41$	−1.47321	−	9.06503i	−0.230077	−	1.41572i	0.572859	−	0.819654i	$-0.305834\pi$
$42$	4.55313	−	1.93991i	0.702562	−	0.299334i
$43$	−7.84941	+	4.96367i	−1.19702	+	0.756952i	−0.975884	−	0.218290i	$-0.929952\pi$
$43$	−7.84941	+	4.96367i	−1.19702	+	0.756952i	−0.221140	+	0.975242i	$0.570978\pi$
$44$	1.99546	−	2.25241i	0.300827	−	0.339563i
$45$	−0.241433	−	2.99068i	−0.0359907	−	0.445825i
$46$	−0.369241	−	1.10601i	−0.0544416	−	0.163072i
$47$	−0.787002	−	0.0955593i	−0.114796	−	0.0139388i	0.0629370	−	0.998018i	$-0.479953\pi$
$47$	−0.787002	−	0.0955593i	−0.114796	−	0.0139388i	−0.177733	+	0.984079i	$0.556876\pi$
$48$	−3.92004	−	2.94572i	−0.565810	−	0.425178i
$49$	0.252034	−	0.308686i	0.0360049	−	0.0440980i
$50$	5.64116	+	4.60586i	0.797780	+	0.651367i
$51$	0.409786	+	0.593678i	0.0573816	+	0.0831316i
$52$	0.266293	−	4.71826i	0.0369281	−	0.654305i
$53$	7.31357	−	10.5955i	1.00460	−	1.45541i	0.117917	−	0.993023i	$-0.462378\pi$
$53$	7.31357	−	10.5955i	1.00460	−	1.45541i	0.886679	−	0.462385i	$-0.153006\pi$
$54$	−1.74769	+	0.506225i	−0.237831	+	0.0688885i
$55$	−5.82215	−	3.68170i	−0.785059	−	0.496441i
$56$	−3.36732	−	0.547242i	−0.449977	−	0.0731283i
$57$	−1.60944	−	0.610382i	−0.213176	−	0.0808470i
$58$	2.82292	−	6.62563i	0.370667	−	0.869988i
$59$	−6.27807	−	6.03017i	−0.817335	−	0.785061i	0.162110	−	0.986773i	$-0.448170\pi$
$59$	−6.27807	−	6.03017i	−0.817335	−	0.785061i	−0.979445	+	0.201712i	$0.935350\pi$
$60$	1.82758	−	3.48216i	0.235939	−	0.449545i
$61$	−4.52213	+	0.365064i	−0.579000	+	0.0467417i	−0.366498	−	0.930419i	$-0.619443\pi$
$61$	−4.52213	+	0.365064i	−0.579000	+	0.0467417i	−0.212502	+	0.977161i	$0.568161\pi$
$62$	3.86987	+	13.3603i	0.491474	+	1.69676i
$63$	−1.96168	+	1.88422i	−0.247149	+	0.237390i
$64$	−0.660547	−	1.74172i	−0.0825683	−	0.217715i
$65$	−10.7589	+	1.13090i	−1.33447	+	0.140270i
$66$	−1.48133	+	3.90595i	−0.182339	+	0.480789i
$67$	0.135153	+	0.317215i	0.0165115	+	0.0387540i	0.928031	−	0.372503i	$-0.121500\pi$
$67$	0.135153	+	0.317215i	0.0165115	+	0.0387540i	−0.911520	+	0.411257i	$0.865090\pi$
$68$	0.0380714	+	0.944731i	0.00461683	+	0.114565i
$69$	0.405293	+	0.496394i	0.0487915	+	0.0597588i
$70$		−	14.8495i		−	1.77486i
$71$	−1.91642	+	1.56471i	−0.227438	+	0.185697i	−0.739312	−	0.673364i	$-0.764849\pi$
$71$	−1.91642	+	1.56471i	−0.227438	+	0.185697i	0.511874	+	0.859061i	$0.328951\pi$
$72$	1.20470	+	0.348945i	0.141975	+	0.0411236i
$73$	−3.27141	−	3.69266i	−0.382890	−	0.432193i	0.525194	−	0.850983i	$-0.323993\pi$
$73$	−3.27141	−	3.69266i	−0.382890	−	0.432193i	−0.908083	+	0.418790i	$0.862454\pi$
$74$	1.66346	−	1.73185i	0.193373	−	0.201323i
$75$	−3.79649	−	1.26746i	−0.438381	−	0.146353i
$76$	−1.35533	−	1.80362i	−0.155467	−	0.206889i
$77$	0.752730	+	6.19929i	0.0857816	+	0.706475i
$78$	1.97701	+	6.25543i	0.223852	+	0.708288i
$79$	−0.845391	+	6.96242i	−0.0951139	+	0.783333i	0.864621	+	0.502425i	$0.167559\pi$
$79$	−0.845391	+	6.96242i	−0.0951139	+	0.783333i	−0.959735	+	0.280908i	$0.909364\pi$
$80$	−12.7413	+	7.35622i	−1.42453	+	0.822450i
$81$	0.799443	−	0.600742i	0.0888270	−	0.0667491i
$82$	−0.672864	+	16.6969i	−0.0743054	+	1.84387i
$83$	−2.53465	+	0.961265i	−0.278214	+	0.105513i	−0.489765	−	0.871854i	$-0.662918\pi$
$83$	−2.53465	+	0.961265i	−0.278214	+	0.105513i	0.211552	+	0.977367i	$0.432148\pi$
$84$	−3.49306	+	0.713113i	−0.381124	+	0.0778070i
$85$	2.12067	−	0.432939i	0.230019	−	0.0469588i
$86$	15.8001	−	5.99221i	1.70377	−	0.646156i
$87$	−0.159378	+	3.95492i	−0.0170871	+	0.424012i
$88$	2.30201	−	1.72985i	0.245396	−	0.184403i
$89$	10.5060	−	6.06567i	1.11364	−	0.642960i	0.173870	−	0.984769i	$-0.444373\pi$
$89$	10.5060	−	6.06567i	1.11364	−	0.642960i	0.939769	+	0.341809i	$0.111040\pi$
$90$	−0.658051	+	5.41954i	−0.0693647	+	0.571269i
$91$	6.96265	+	6.90667i	0.729884	+	0.724016i
$92$	0.101243	+	0.833813i	0.0105553	+	0.0869310i
$93$	−4.59241	−	6.11139i	−0.476211	−	0.633721i
$94$	1.36826	+	0.456791i	0.141125	+	0.0471144i
$95$	−3.57765	+	3.72473i	−0.367059	+	0.382149i
$96$	4.25299	+	4.80063i	0.434069	+	0.489963i
$97$	12.1748	+	3.52648i	1.23617	+	0.358060i	0.831046	−	0.556203i	$-0.187742\pi$
$97$	12.1748	+	3.52648i	1.23617	+	0.358060i	0.405121	+	0.914263i	$0.367230\pi$
$98$	−0.561663	+	0.458584i	−0.0567366	+	0.0463240i
$99$		−	2.29587i		−	0.230744i
$100$	−3.31782	−	4.06359i	−0.331782	−	0.406359i
$101$	−0.745598	−	18.5018i	−0.0741897	−	1.84100i	−0.425758	−	0.904837i	$-0.639993\pi$
$101$	−0.745598	−	18.5018i	−0.0741897	−	1.84100i	0.351568	−	0.936162i	$-0.385648\pi$
$102$	−0.514480	−	1.20753i	−0.0509411	−	0.119563i
$103$	−0.390952	+	1.03086i	−0.0385216	+	0.101573i	−0.952897	−	0.303295i	$-0.901913\pi$
$103$	−0.390952	+	1.03086i	−0.0385216	+	0.101573i	0.914375	+	0.404868i	$0.132683\pi$
$104$	1.15278	−	4.37274i	0.113039	−	0.428783i
$105$	2.89399	+	7.63084i	0.282425	+	0.744693i
$106$	−16.8946	+	16.2275i	−1.64095	+	1.57615i
$107$	1.85063	+	6.38911i	0.178907	+	0.617658i	0.998970	+	0.0453845i	$0.0144513\pi$
$107$	1.85063	+	6.38911i	0.178907	+	0.617658i	−0.820063	+	0.572274i	$0.806062\pi$
$108$	1.30644	−	0.105467i	0.125712	−	0.0101486i
$109$	3.97773	−	7.57893i	0.380997	−	0.725930i	−0.617145	−	0.786849i	$-0.711711\pi$
$109$	3.97773	−	7.57893i	0.380997	−	0.725930i	0.998143	+	0.0609194i	$0.0194033\pi$
$110$	9.03952	+	8.68258i	0.861885	+	0.827852i
$111$	−0.517299	+	1.21415i	−0.0490999	+	0.115242i
$112$	12.4708	+	4.72956i	1.17838	+	0.446901i
$113$	14.7929	+	2.40407i	1.39160	+	0.226156i	0.809574	−	0.587017i	$-0.199698\pi$
$113$	14.7929	+	2.40407i	1.39160	+	0.226156i	0.582021	+	0.813174i	$0.302262\pi$
$114$	2.64710	+	1.67393i	0.247924	+	0.156777i
$115$	1.84685	−	0.534948i	0.172220	−	0.0498841i
$116$	−2.94706	+	4.26955i	−0.273627	+	0.396418i
$117$	−2.23505	−	2.82923i	−0.206630	−	0.261563i
$118$	8.99759	+	13.0353i	0.828295	+	1.19999i
$119$	−1.51989	−	1.24095i	−0.139328	−	0.113758i
$120$	2.38000	−	2.91497i	0.217263	−	0.266099i
$121$	4.57998	+	3.44163i	0.416362	+	0.312875i
$122$	8.19474	+	0.995021i	0.741917	+	0.0900850i
$123$	−2.90827	−	8.71132i	−0.262230	−	0.785473i
$124$	−0.806248	−	9.98717i	−0.0724032	−	0.896875i
$125$	1.98472	−	2.24029i	0.177519	−	0.200377i
$126$	4.18298	−	2.64516i	0.372650	−	0.235649i
$127$	13.2591	−	5.64916i	1.17655	−	0.501282i	0.286918	−	0.957955i	$-0.407369\pi$
$127$	13.2591	−	5.64916i	1.17655	−	0.501282i	0.889635	+	0.456673i	$0.150959\pi$
$128$	−1.51393	−	9.31558i	−0.133814	−	0.823389i
$129$	−6.95153	+	6.15852i	−0.612048	+	0.542228i
$130$	19.5921	+	1.89960i	1.71834	+	0.166606i
$131$	15.2165	+	13.4807i	1.32947	+	1.17781i	0.969568	+	0.244823i	$0.0787298\pi$
$131$	15.2165	+	13.4807i	1.32947	+	1.17781i	0.359906	+	0.932989i	$0.382809\pi$
$132$	1.60831	−	2.54333i	0.139985	−	0.221369i
$133$	4.66679	+	0.376742i	0.404662	+	0.0326677i
$134$	−0.125494	−	0.614708i	−0.0108410	−	0.0531027i
$135$	−0.718046	−	2.91323i	−0.0617995	−	0.250731i
$136$	−0.145133	+	0.893042i	−0.0124451	+	0.0765777i
$137$	3.83972	+	6.07203i	0.328050	+	0.518769i	0.968429	−	0.249290i	$-0.0801972\pi$
$137$	3.83972	+	6.07203i	0.328050	+	0.518769i	−0.640379	+	0.768059i	$0.721223\pi$
$138$	−0.541876	−	1.03246i	−0.0461275	−	0.0878886i
$139$	−3.81760	+	13.1799i	−0.323805	+	1.11790i	0.619230	+	0.785210i	$0.287445\pi$
$139$	−3.81760	+	13.1799i	−0.323805	+	1.11790i	−0.943035	+	0.332694i	$0.892042\pi$
$140$	−2.13963	+	10.4806i	−0.180832	+	0.885774i
$141$	−0.792139	+	0.0319221i	−0.0667102	+	0.00268833i
$142$	3.98600	−	2.09201i	0.334498	−	0.175558i
$143$	−8.27547	+	0.200096i	−0.692030	+	0.0167329i
$144$	−4.34181	−	2.27876i	−0.361817	−	0.189896i
$145$	10.7294	+	5.09116i	0.891028	+	0.422798i
$146$	4.48818	+	7.77376i	0.371445	+	0.643361i
$147$	0.199254	−	0.345118i	0.0164342	−	0.0284648i
$148$	−1.42359	+	0.982633i	−0.117018	+	0.0807719i
$149$	−8.59958	+	11.4440i	−0.704505	+	0.937526i	−0.999840	−	0.0178678i	$-0.994312\pi$
$149$	−8.59958	+	11.4440i	−0.704505	+	0.937526i	0.295335	+	0.955394i	$0.404569\pi$
$150$	6.30694	+	3.64131i	0.514959	+	0.297312i
$151$	10.4862	−	1.27325i	0.853352	−	0.103616i	0.317841	−	0.948144i	$-0.397042\pi$
$151$	10.4862	−	1.27325i	0.853352	−	0.103616i	0.535511	+	0.844528i	$0.320119\pi$
$152$	−0.925498	−	1.95045i	−0.0750678	−	0.158202i
$153$	0.499713	+	0.520256i	0.0403994	+	0.0420602i
$154$	0.914313	−	11.3258i	0.0736775	−	0.912659i
$155$	−22.2703	+	5.48914i	−1.78880	+	0.440899i
$156$	−0.494018	−	4.69988i	−0.0395531	−	0.376291i
$157$	4.19209	+	1.03326i	0.334565	+	0.0824629i	0.403020	−	0.915191i	$-0.367961\pi$
$157$	4.19209	+	1.03326i	0.334565	+	0.0824629i	−0.0684545	+	0.997654i	$0.521807\pi$
$158$	4.04112	−	12.1046i	0.321494	−	0.962993i
$159$	5.51922	−	11.6315i	0.437702	−	0.922438i
$160$	18.2531	−	6.09377i	1.44303	−	0.481754i
$161$	−1.43453	−	0.990184i	−0.113057	−	0.0780374i
$162$	−1.64386	+	0.780019i	−0.129154	+	0.0612841i
$163$	−5.74038	−	0.231329i	−0.449621	−	0.0181191i	−0.185577	−	0.982630i	$-0.559415\pi$
$163$	−5.74038	−	0.231329i	−0.449621	−	0.0181191i	−0.264044	+	0.964511i	$0.585057\pi$
$164$	2.88073	−	11.6876i	0.224947	−	0.912645i
$165$	−6.33734	−	2.70009i	−0.493361	−	0.210202i
$166$	4.86852	−	0.791212i	0.377871	−	0.0614100i
$167$	21.9974	+	4.49080i	1.70221	+	0.347508i	0.950199	−	0.311644i	$-0.100880\pi$
$167$	21.9974	+	4.49080i	1.70221	+	0.347508i	0.752009	+	0.659153i	$0.229085\pi$
$168$	−3.41149			−0.263203
$169$	−10.0032	+	8.30281i	−0.769474	+	0.638678i
$170$	−3.93822			−0.302048
$171$	−1.68651	−	0.344304i	−0.128971	−	0.0263296i
$172$	−12.0150	+	1.95262i	−0.916133	+	0.148886i
$173$	−0.355474	−	0.151453i	−0.0270262	−	0.0115148i	0.378411	−	0.925638i	$-0.376471\pi$
$173$	−0.355474	−	0.151453i	−0.0270262	−	0.0115148i	−0.405437	+	0.914123i	$0.632881\pi$
$174$	1.72354	−	6.99266i	0.130661	−	0.530112i
$175$	10.8780	+	0.438368i	0.822298	+	0.0331375i
$176$	−10.1708	+	4.82611i	−0.766654	+	0.363782i
$177$	−7.16408	−	4.94501i	−0.538485	−	0.371689i
$178$	−20.9374	+	6.98992i	−1.56932	+	0.523917i
$179$	0.507603	−	1.06975i	0.0379400	−	0.0799570i	−0.883595	−	0.468251i	$-0.844884\pi$
$179$	0.507603	−	1.06975i	0.0379400	−	0.0799570i	0.921535	+	0.388294i	$0.126936\pi$
$180$	1.24533	−	3.73023i	0.0928217	−	0.278035i
$181$	−22.0593	−	5.43712i	−1.63965	−	0.404138i	−0.691608	−	0.722273i	$-0.743097\pi$
$181$	−22.0593	−	5.43712i	−1.63965	−	0.404138i	−0.948045	+	0.318135i	$0.896944\pi$
$182$	−9.89903	−	14.8470i	−0.733765	−	1.10053i
$183$	−4.40501	+	1.08574i	−0.325628	+	0.0802600i
$184$	−0.0646746	+	0.801139i	−0.00476788	+	0.0590608i
$185$	2.74305	+	2.85582i	0.201673	+	0.209964i
$186$	5.96290	+	12.5666i	0.437221	+	0.921424i
$187$	1.64411	−	0.199631i	0.120229	−	0.0145984i
$188$	−0.899881	−	0.519547i	−0.0656306	−	0.0378918i
$189$	−1.63403	+	2.17450i	−0.118858	+	0.158172i
$190$	7.73372	−	5.33820i	0.561063	−	0.387274i
$191$	12.0906	−	20.9416i	0.874849	−	1.51528i	0.0179245	−	0.999839i	$-0.494294\pi$
$191$	12.0906	−	20.9416i	0.874849	−	1.51528i	0.856924	−	0.515443i	$-0.172373\pi$
$192$	−0.931384	−	1.61320i	−0.0672168	−	0.116423i
$193$	8.87010	+	4.20891i	0.638484	+	0.302964i	0.720279	−	0.693685i	$-0.244014\pi$
$193$	8.87010	+	4.20891i	0.638484	+	0.302964i	−0.0817949	+	0.996649i	$0.526065\pi$
$194$	−20.4213	−	10.7179i	−1.46617	−	0.769503i
$195$	−10.4381	+	2.84210i	−0.747490	+	0.203527i
$196$	0.462492	−	0.242734i	0.0330351	−	0.0173382i
$197$	−8.23527	+	0.331870i	−0.586739	+	0.0236448i	−0.331861	−	0.943328i	$-0.607676\pi$
$197$	−8.23527	+	0.331870i	−0.586739	+	0.0236448i	−0.254878	+	0.966973i	$0.582035\pi$
$198$	−0.835590	+	4.09299i	−0.0593828	+	0.290876i
$199$	3.87163	−	13.3664i	0.274452	−	0.947519i	−0.698326	−	0.715780i	$-0.746071\pi$
$199$	3.87163	−	13.3664i	0.274452	−	0.947519i	0.972778	−	0.231739i	$-0.0744416\pi$
$200$	−2.33290	−	4.44496i	−0.164961	−	0.314306i
$201$	0.184288	+	0.291427i	0.0129986	+	0.0205557i
$202$	−5.40457	+	33.2556i	−0.380264	+	2.33986i
$203$	−2.57652	−	10.4533i	−0.180836	−	0.733681i
$204$	0.189124	+	0.926390i	0.0132413	+	0.0648603i
$205$	−27.4663	−	2.21731i	−1.91833	−	0.154864i
$206$	1.07216	−	1.69548i	0.0747007	−	0.118130i
$207$	0.479671	+	0.424952i	0.0333395	+	0.0295362i
$208$	−7.83536	+	15.8486i	−0.543285	+	1.09891i
$209$	−2.95803	+	2.62059i	−0.204611	+	0.181270i
$210$	−2.38203	−	14.6572i	−0.164376	−	1.01144i
$211$	−6.95938	+	2.96512i	−0.479104	+	0.204127i	−0.617997	−	0.786180i	$-0.712056\pi$
$211$	−6.95938	+	2.96512i	−0.479104	+	0.204127i	0.138893	+	0.990307i	$0.455645\pi$
$212$	14.2622	−	9.01887i	0.979532	−	0.619419i
$213$	−1.64061	+	1.85186i	−0.112413	+	0.126888i
$214$	−0.973889	−	12.0638i	−0.0665737	−	0.824663i
$215$	8.82404	+	26.4312i	0.601795	+	1.80260i
$216$	1.24507	+	0.151179i	0.0847164	+	0.0102864i
$217$	16.6231	+	12.4914i	1.12845	+	0.847975i
$218$	−9.84971	+	12.0637i	−0.667106	+	0.817057i
$219$	−3.82139	−	3.12007i	−0.258226	−	0.210835i
$220$	−5.12894	−	7.43055i	−0.345793	−	0.500968i
$221$	1.83171	−	1.84656i	0.123214	−	0.124213i
$222$	1.36411	−	1.97626i	0.0915532	−	0.132638i
$223$	10.2524	−	2.96964i	0.686551	−	0.198862i	0.0834324	−	0.996513i	$-0.473412\pi$
$223$	10.2524	−	2.96964i	0.686551	−	0.198862i	0.603119	+	0.797652i	$0.293925\pi$
$224$	−14.7444	−	9.32379i	−0.985152	−	0.622972i
$225$	−3.95064	−	0.642042i	−0.263376	−	0.0428028i
$226$	−25.4971	−	9.66979i	−1.69605	−	0.643225i
$227$	−2.63530	+	6.18528i	−0.174911	+	0.410531i	−0.984243	−	0.176820i	$-0.943419\pi$
$227$	−2.63530	+	6.18528i	−0.174911	+	0.410531i	0.809332	+	0.587351i	$0.199829\pi$
$228$	−1.62710	−	1.56285i	−0.107757	−	0.103502i
$229$	8.63130	−	16.4456i	0.570372	−	1.08675i	−0.413938	−	0.910305i	$-0.635847\pi$
$229$	8.63130	−	16.4456i	0.570372	−	1.08675i	0.984310	−	0.176448i	$-0.0564608\pi$
$230$	−3.48719	+	0.281515i	−0.229939	+	0.0185626i
$231$	1.73742	+	5.99827i	0.114314	+	0.394657i
$232$	−3.58030	+	3.43893i	−0.235058	+	0.225777i
$233$	−0.673542	−	1.77599i	−0.0441252	−	0.116349i	0.911142	−	0.412092i	$-0.135202\pi$
$233$	−0.673542	−	1.77599i	−0.0441252	−	0.116349i	−0.955267	+	0.295744i	$0.904433\pi$
$234$	2.95485	+	5.85729i	0.193164	+	0.382903i
$235$	−0.843489	+	2.22410i	−0.0550232	+	0.145084i
$236$	−4.47217	−	10.4966i	−0.291114	−	0.683269i
$237$	0.282407	+	7.00787i	0.0183443	+	0.455210i
$238$	2.25795	+	2.76549i	0.146361	+	0.179260i
$239$			4.05944i			0.262583i	0.991344	+	0.131292i	$0.0419125\pi$
$239$			4.05944i			0.262583i	−0.991344	+	0.131292i	$0.958088\pi$
$240$	−11.3963	+	9.30481i	−0.735630	+	0.600623i
$241$	25.6265	+	7.42280i	1.65075	+	0.478144i	0.967673	−	0.252206i	$-0.0811562\pi$
$241$	25.6265	+	7.42280i	1.65075	+	0.478144i	0.683072	+	0.730351i	$0.260643\pi$
$242$	−6.91241	−	7.80249i	−0.444346	−	0.501563i
$243$	0.692724	−	0.721202i	0.0444383	−	0.0462652i
$244$	−5.64038	−	1.88304i	−0.361088	−	0.120549i
$245$	−0.718299	−	0.955883i	−0.0458905	−	0.0610691i
$246$	2.01423	+	16.5887i	0.128423	+	1.05765i
$247$	−1.09406	+	6.10905i	−0.0696132	+	0.388709i
$248$	1.15570	−	9.51803i	0.0733869	−	0.604395i
$249$	−2.34763	+	1.35540i	−0.148775	+	0.0858952i
$250$	−4.35364	+	3.27154i	−0.275348	+	0.206911i
$251$	−0.382570	+	9.49338i	−0.0241476	+	0.599217i	0.941138	+	0.338022i	$0.109758\pi$
$251$	−0.382570	+	9.49338i	−0.0241476	+	0.599217i	−0.965286	+	0.261195i	$0.915883\pi$
$252$	−3.33343	+	1.26420i	−0.209987	+	0.0796374i
$253$	1.44154	−	0.294293i	0.0906290	−	0.0185020i
$254$	−25.6938	+	5.24542i	−1.61217	+	0.329127i
$255$	2.02376	−	0.767512i	0.126733	−	0.0480635i
$256$	−0.841474	+	20.8810i	−0.0525921	+	1.30506i
$257$	6.80117	−	5.11075i	0.424245	−	0.318800i	−0.367086	−	0.930187i	$-0.619645\pi$
$257$	6.80117	−	5.11075i	0.424245	−	0.318800i	0.791332	+	0.611387i	$0.209388\pi$
$258$	14.6343	−	8.44913i	0.911093	−	0.526020i
$259$	0.432697	−	3.56358i	0.0268865	−	0.221430i
$260$	−13.5541	−	4.16370i	−0.840592	−	0.258221i
$261$	0.477100	+	3.92927i	0.0295317	+	0.243216i
$262$	−22.2211	−	29.5709i	−1.37282	−	1.82690i
$263$	8.03622	+	2.68289i	0.495535	+	0.165434i	0.553441	−	0.832888i	$-0.313314\pi$
$263$	8.03622	+	2.68289i	0.495535	+	0.165434i	−0.0579065	+	0.998322i	$0.518443\pi$
$264$	1.99472	−	2.07672i	0.122766	−	0.127813i
$265$	−25.6157	−	28.9142i	−1.57356	−	1.77618i
$266$	−8.18265	−	2.37013i	−0.501710	−	0.145322i
$267$	9.39700	−	7.67241i	0.575087	−	0.469544i
$268$			0.451936i			0.0276064i
$269$	−16.4673	−	20.1688i	−1.00403	−	1.22971i	−0.973146	−	0.230191i	$-0.926065\pi$
$269$	−16.4673	−	20.1688i	−1.00403	−	1.22971i	−0.0308847	−	0.999523i	$-0.509832\pi$
$270$	0.219826	+	5.45491i	0.0133782	+	0.331976i
$271$	−7.47968	−	17.5555i	−0.454358	−	1.06642i	−0.976879	−	0.213792i	$-0.931419\pi$
$271$	−7.47968	−	17.5555i	−0.454358	−	1.06642i	0.522521	−	0.852626i	$-0.324992\pi$
$272$	1.25432	−	3.30737i	0.0760543	−	0.200539i
$273$	7.98039	+	5.70034i	0.482995	+	0.345000i
$274$	−4.63536	−	12.2225i	−0.280033	−	0.738385i
$275$	−6.62726	+	6.36557i	−0.399639	+	0.383858i
$276$	0.233685	+	0.806774i	0.0140662	+	0.0485621i
$277$	27.6888	−	2.23527i	1.66366	−	0.134305i	0.787497	−	0.616319i	$-0.211377\pi$
$277$	27.6888	−	2.23527i	1.66366	−	0.134305i	0.876163	+	0.482015i	$0.160095\pi$
$278$	11.6027	−	22.1071i	0.695885	−	1.32590i
$279$	−5.51328	−	5.29557i	−0.330071	−	0.317038i
$280$	−4.01213	+	9.41681i	−0.239770	+	0.562762i
$281$	−22.9778	−	8.71433i	−1.37074	−	0.519853i	−0.444159	−	0.895948i	$-0.646497\pi$
$281$	−22.9778	−	8.71433i	−1.37074	−	0.519853i	−0.926581	+	0.376095i	$0.877267\pi$
$282$	1.42381	+	0.231392i	0.0847868	+	0.0137792i
$283$	−13.6570	−	8.63619i	−0.811827	−	0.513368i	0.0628798	−	0.998021i	$-0.479972\pi$
$283$	−13.6570	−	8.63619i	−0.811827	−	0.513368i	−0.874707	+	0.484653i	$0.838946\pi$
$284$	−3.11471	+	0.902186i	−0.184824	+	0.0535349i
$285$	−2.93383	+	4.25039i	−0.173785	+	0.251772i
$286$	14.8260	+	2.65516i	0.876680	+	0.157003i
$287$	14.1906	+	20.5586i	0.837643	+	1.21354i
$288$	4.96799	+	4.05624i	0.292742	+	0.239016i
$289$	10.4225	−	12.7652i	0.613086	−	0.750894i
$290$	−17.2750	−	12.9813i	−1.01442	−	0.762289i
$291$	12.5829	+	1.52784i	0.737620	+	0.0895633i
$292$	−2.04760	−	6.13332i	−0.119827	−	0.358926i
$293$	0.0659441	+	0.816865i	0.00385250	+	0.0477218i	0.998398	−	0.0565826i	$-0.0180204\pi$
$293$	0.0659441	+	0.816865i	0.00385250	+	0.0477218i	−0.994545	+	0.104304i	$0.966738\pi$
$294$	−0.480828	+	0.542742i	−0.0280425	+	0.0316534i
$295$	−22.0752	+	13.9595i	−1.28527	+	0.812753i
$296$	−1.52280	+	0.648806i	−0.0885111	+	0.0377111i
$297$	−0.368284	−	2.26614i	−0.0213700	−	0.131495i
$298$	19.4960	−	17.2720i	1.12938	−	1.00054i
$299$	1.48993	−	1.76601i	0.0861650	−	0.102131i
$300$	−3.92670	−	3.47875i	−0.226708	−	0.200846i
$301$	13.5013	−	21.3505i	0.778200	−	1.23063i
$302$	−19.1577	−	1.54657i	−1.10240	−	0.0889952i
$303$	−3.70384	−	18.1426i	−0.212780	−	1.04227i
$304$	2.01991	+	8.19509i	0.115850	+	0.470020i
$305$	−2.18358	+	13.4361i	−0.125032	+	0.769350i
$306$	−0.701519	−	1.10936i	−0.0401031	−	0.0634180i
$307$	−4.42622	−	8.43345i	−0.252617	−	0.481322i	0.725815	−	0.687890i	$-0.241463\pi$
$307$	−4.42622	−	8.43345i	−0.252617	−	0.481322i	−0.978432	+	0.206568i	$0.933771\pi$
$308$	−2.27722	+	7.86188i	−0.129757	+	0.447972i
$309$	−0.220528	+	1.08022i	−0.0125454	+	0.0614515i
$310$	41.7004	−	1.68047i	2.36842	−	0.0954443i
$311$	10.4350	−	5.47669i	0.591712	−	0.310555i	−0.142158	−	0.989844i	$-0.545404\pi$
$311$	10.4350	−	5.47669i	0.591712	−	0.310555i	0.733870	+	0.679289i	$0.237712\pi$
$312$	0.436411	−	4.50104i	0.0247069	−	0.254821i
$313$	−13.3259	−	6.99396i	−0.753223	−	0.395322i	0.0439804	−	0.999032i	$-0.485996\pi$
$313$	−13.3259	−	6.99396i	−0.753223	−	0.395322i	−0.797204	+	0.603710i	$0.793688\pi$
$314$	−7.09743	−	3.36777i	−0.400531	−	0.190054i
$315$	4.08059	+	7.06779i	0.229915	+	0.398225i
$316$	−4.59631	+	7.96104i	−0.258562	+	0.447843i
$317$	−21.0121	+	14.5036i	−1.18016	+	0.814605i	−0.986062	−	0.166377i	$-0.946793\pi$
$317$	−21.0121	+	14.5036i	−1.18016	+	0.814605i	−0.194097	+	0.980982i	$0.562178\pi$
$318$	−14.0728	+	18.7274i	−0.789161	+	1.05018i
$319$	7.86989	+	4.54368i	0.440629	+	0.254397i
$320$	−5.54832	+	0.673688i	−0.310161	+	0.0376603i
$321$	2.85155	+	6.00951i	0.159158	+	0.335418i
$322$	2.19704	+	2.28736i	0.122436	+	0.127470i
$323$	0.0999153	−	1.23767i	0.00555944	−	0.0688660i
$324$	1.27261	−	0.313669i	0.0707003	−	0.0174261i
$325$	−1.96992	+	14.2960i	−0.109272	+	0.793002i
$326$	10.1495	+	2.50163i	0.562130	+	0.138553i
$327$	2.71047	−	8.11886i	0.149889	−	0.448974i
$328$	4.93797	−	10.4066i	0.272654	−	0.574606i
$329$	2.04541	−	0.682858i	0.112767	−	0.0376472i
$330$	10.3152	+	7.12010i	0.567836	+	0.391949i
$331$	2.55068	−	1.21031i	0.140198	−	0.0665247i	−0.357301	−	0.933989i	$-0.616303\pi$
$331$	2.55068	−	1.21031i	0.140198	−	0.0665247i	0.497499	+	0.867464i	$0.334252\pi$
$332$	−3.55015	−	0.143066i	−0.194840	−	0.00785178i
$333$	−0.315838	+	1.28140i	−0.0173078	+	0.0702205i
$334$	−37.5816	−	16.0120i	−2.05637	−	0.876139i
$335$	1.02117	−	0.165956i	0.0557923	−	0.00906712i
$336$	13.0680	+	2.66785i	0.712917	+	0.145543i
$337$	22.0758			1.20254			0.601272	−	0.799044i	$-0.294661\pi$
$337$	22.0758			1.20254			0.601272	+	0.799044i	$0.294661\pi$
$338$	20.8551	−	11.1612i	1.13437	−	0.607091i
$339$	14.9869			0.813979
$340$	2.77955	+	0.567449i	0.150742	+	0.0307743i
$341$	−17.3237	+	2.81537i	−0.938129	+	0.152461i
$342$	2.88134	+	1.22762i	0.155805	+	0.0663823i
$343$	4.29720	−	17.4344i	0.232027	−	0.941370i
$344$	−11.6387	−	0.469022i	−0.627514	−	0.0252880i
$345$	1.73713	−	0.824276i	0.0935237	−	0.0443775i
$346$	0.578603	+	0.399381i	0.0311059	+	0.0214709i
$347$	21.9584	−	7.33080i	1.17879	−	0.393538i	0.341281	−	0.939961i	$-0.389139\pi$
$347$	21.9584	−	7.33080i	1.17879	−	0.393538i	0.837509	+	0.546424i	$0.184011\pi$
$348$	−2.22401	+	4.68700i	−0.119219	+	0.251250i
$349$	−9.11816	+	27.3122i	−0.488084	+	1.46199i	0.360415	+	0.932792i	$0.382635\pi$
$349$	−9.11816	+	27.3122i	−0.488084	+	1.46199i	−0.848499	+	0.529197i	$0.822493\pi$
$350$	−19.2333	−	4.74058i	−1.02806	−	0.253394i
$351$	−2.65995	−	2.43407i	−0.141977	−	0.129921i
$352$	14.2969	−	3.52387i	0.762027	−	0.187823i
$353$	0.174838	−	2.16576i	0.00930569	−	0.115272i	−0.990437	−	0.137968i	$-0.955943\pi$
$353$	0.174838	−	2.16576i	0.00930569	−	0.115272i	0.999742	+	0.0226961i	$0.00722502\pi$
$354$	10.9721	+	11.4231i	0.583159	+	0.607133i
$355$	3.18228	+	6.70651i	0.168898	+	0.355944i
$356$	15.7845	−	1.91659i	0.836578	−	0.101579i
$357$	−1.69927	−	0.981074i	−0.0899349	−	0.0519240i
$358$	−1.29427	+	1.72237i	−0.0684045	+	0.0910298i
$359$	−3.98056	+	2.74758i	−0.210086	+	0.145012i	−0.668461	−	0.743747i	$-0.733047\pi$
$359$	−3.98056	+	2.74758i	−0.210086	+	0.145012i	0.458376	+	0.888759i	$0.348431\pi$
$360$	1.88158	−	3.25900i	0.0991682	−	0.171764i
$361$	−8.01856	−	13.8886i	−0.422030	−	0.730977i
$362$	37.3475	+	17.7216i	1.96294	+	0.931428i
$363$	5.07274	+	2.66238i	0.266250	+	0.139739i
$364$	4.84735	+	11.9052i	0.254070	+	0.624001i
$365$	−13.1066	+	6.87886i	−0.686029	+	0.360056i
$366$	8.24823	−	0.332392i	0.431142	−	0.0173744i
$367$	−5.18184	+	25.3823i	−0.270490	+	1.32495i	0.586641	+	0.809847i	$0.300450\pi$
$367$	−5.18184	+	25.3823i	−0.270490	+	1.32495i	−0.857131	+	0.515099i	$0.827755\pi$
$368$	0.874246	−	3.01825i	0.0455732	−	0.157337i
$369$	−4.26800	−	8.13199i	−0.222183	−	0.423335i
$370$	−3.85082	−	6.08958i	−0.200195	−	0.316582i
$371$	−5.61744	+	34.5655i	−0.291643	+	1.79455i
$372$	−2.39786	−	9.72851i	−0.124323	−	0.504400i
$373$	5.58719	+	27.3679i	0.289294	+	1.41706i	0.821388	+	0.570370i	$0.193200\pi$
$373$	5.58719	+	27.3679i	0.289294	+	1.41706i	−0.532094	+	0.846685i	$0.678595\pi$
$374$	−3.00370	−	0.242484i	−0.155318	−	0.0125385i
$375$	1.59965	−	2.52965i	0.0826056	−	0.130630i
$376$	−0.744260	−	0.659357i	−0.0383823	−	0.0340037i
$377$	14.1215	−	2.06216i	0.727292	−	0.106207i
$378$	3.70450	−	3.28190i	0.190539	−	0.168803i
$379$	3.42932	+	21.1014i	0.176152	+	1.08391i	0.913033	+	0.407886i	$0.133734\pi$
$379$	3.42932	+	21.1014i	0.176152	+	1.08391i	−0.736881	+	0.676023i	$0.763702\pi$
$380$	−6.22754	+	2.65331i	−0.319466	+	0.136112i
$381$	12.1812	−	7.70291i	0.624061	−	0.394632i
$382$	−29.1765	+	32.9334i	−1.49280	+	1.68502i
$383$	0.173502	+	2.14921i	0.00886553	+	0.109819i	0.999676	−	0.0254347i	$-0.00809700\pi$
$383$	0.173502	+	2.14921i	0.00886553	+	0.109819i	−0.990811	+	0.135254i	$0.956815\pi$
$384$	−2.98865	−	8.95210i	−0.152514	−	0.456835i
$385$	18.6004	+	2.25850i	0.947966	+	0.115104i
$386$	−14.2814	−	10.7318i	−0.726904	−	0.546233i
$387$	−5.87362	+	7.19387i	−0.298573	+	0.365685i
$388$	12.8688	+	10.5071i	0.653315	+	0.533415i
$389$	−11.9709	−	17.3429i	−0.606950	−	0.879320i	0.392227	−	0.919868i	$-0.371705\pi$
$389$	−11.9709	−	17.3429i	−0.606950	−	0.879320i	−0.999178	+	0.0405488i	$0.987089\pi$
$390$	19.6431	−	1.26778i	0.994665	−	0.0641967i
$391$	−0.262605	+	0.380449i	−0.0132805	+	0.0192402i
$392$	0.480081	−	0.139057i	0.0242478	−	0.00702345i
$393$	17.1819	+	10.8652i	0.866714	+	0.548076i
$394$	14.8023	+	2.40561i	0.745729	+	0.121193i
$395$	19.6761	+	7.46215i	0.990010	+	0.375461i
$396$	1.17950	−	2.76839i	0.0592721	−	0.139117i
$397$	−23.5551	−	22.6250i	−1.18220	−	1.13551i	−0.987984	−	0.154555i	$-0.950606\pi$
$397$	−23.5551	−	22.6250i	−1.18220	−	1.13551i	−0.194211	−	0.980960i	$-0.562215\pi$
$398$	−11.7669	+	22.4200i	−0.589822	+	1.12381i
$399$	4.66679	−	0.376742i	0.233632	−	0.0188607i
$400$	5.46030	+	18.8511i	0.273015	+	0.942557i
$401$	−23.4183	+	22.4936i	−1.16945	+	1.12328i	−0.179228	+	0.983808i	$0.557360\pi$
$401$	−23.4183	+	22.4936i	−1.16945	+	1.12328i	−0.990226	+	0.139469i	$0.955460\pi$
$402$	−0.222474	−	0.586617i	−0.0110960	−	0.0292578i
$403$	−18.6074	+	20.3341i	−0.926899	+	1.01291i
$404$	8.60621	−	22.6927i	0.428175	−	1.12900i
$405$	−1.17606	−	2.76032i	−0.0584390	−	0.137161i
$406$	0.788786	+	19.5735i	0.0391468	+	0.971418i
$407$	1.91630	+	2.34704i	0.0949876	+	0.116339i
$408$			0.904758i			0.0447922i
$409$	−21.1050	+	17.2317i	−1.04357	+	0.852051i	−0.989215	−	0.146470i	$-0.953209\pi$
$409$	−21.1050	+	17.2317i	−1.04357	+	0.852051i	−0.0543583	+	0.998521i	$0.517311\pi$
$410$	48.1588	+	13.9494i	2.37840	+	0.688911i
$411$	4.76402	+	5.37747i	0.234992	+	0.265251i
$412$	−1.00101	+	1.04217i	−0.0493164	+	0.0513438i
$413$	22.4592	+	7.49799i	1.10515	+	0.368952i
$414$	−0.700476	−	0.932165i	−0.0344265	−	0.0458134i
$415$	0.980390	+	8.07423i	0.0481254	+	0.396349i
$416$	14.1877	−	18.2606i	0.695610	−	0.895301i
$417$	−1.65396	+	13.6216i	−0.0809948	+	0.667053i
$418$	6.22723	−	3.59529i	0.304584	−	0.175851i
$419$	14.4011	−	10.8218i	0.703542	−	0.528677i	−0.187688	−	0.982229i	$-0.560100\pi$
$419$	14.4011	−	10.8218i	0.703542	−	0.528677i	0.891230	+	0.453551i	$0.149843\pi$
$420$	−0.430717	+	10.6881i	−0.0210168	+	0.521527i
$421$	4.71808	−	1.78933i	0.229945	−	0.0872067i	−0.236941	−	0.971524i	$-0.576145\pi$
$421$	4.71808	−	1.78933i	0.229945	−	0.0872067i	0.466886	+	0.884317i	$0.345376\pi$
$422$	13.4861	−	2.75320i	0.656492	−	0.134024i
$423$	−0.776761	+	0.158577i	−0.0377674	+	0.00771027i
$424$	15.0981	−	5.72597i	0.733230	−	0.278078i
$425$	0.116259	−	2.88493i	0.00563938	−	0.139940i
$426$	3.59880	−	2.70432i	0.174362	−	0.131025i
$427$	10.6870	−	6.17015i	0.517181	−	0.298595i
$428$	−1.05088	+	8.65480i	−0.0507964	+	0.418346i
$429$	−8.13621	+	1.52498i	−0.392820	+	0.0736269i
$430$	−6.11142	−	50.3321i	−0.294719	−	2.42723i
$431$	−1.60306	−	2.13329i	−0.0772168	−	0.102757i	0.759182	−	0.650879i	$-0.225599\pi$
$431$	−1.60306	−	2.13329i	−0.0772168	−	0.102757i	−0.836398	+	0.548122i	$0.815343\pi$
$432$	−4.65112	−	1.55277i	−0.223777	−	0.0747078i
$433$	−17.9231	+	18.6600i	−0.861331	+	0.896741i	−0.995552	−	0.0942105i	$-0.969967\pi$
$433$	−17.9231	+	18.6600i	−0.861331	+	0.896741i	0.134221	+	0.990951i	$0.457147\pi$
$434$	−25.0887	−	28.3193i	−1.20430	−	1.35937i
$435$	11.4071	+	3.30412i	0.546930	+	0.158420i
$436$	8.69004	−	7.09520i	0.416177	−	0.339798i
$437$		−	1.10307i		−	0.0527669i
$438$	5.67706	+	6.95314i	0.271261	+	0.332234i
$439$	−0.527519	−	13.0903i	−0.0251771	−	0.624764i	−0.961691	−	0.274134i	$-0.911609\pi$
$439$	−0.527519	−	13.0903i	−0.0251771	−	0.624764i	0.936514	−	0.350629i	$-0.114032\pi$
$440$	−3.38650	−	7.94840i	−0.161445	−	0.378925i
$441$	0.141313	−	0.372611i	0.00672917	−	0.0177434i
$442$	−3.93756	+	2.62531i	−0.187290	+	0.124873i
$443$	12.6460	+	33.3449i	0.600831	+	1.58426i	0.797189	+	0.603730i	$0.206319\pi$
$443$	12.6460	+	33.3449i	0.600831	+	1.58426i	−0.196358	+	0.980532i	$0.562911\pi$
$444$	−1.24753	+	1.19827i	−0.0592051	+	0.0568673i
$445$	−10.1268	−	34.9619i	−0.480058	−	1.65735i
$446$	−19.3584	+	1.56277i	−0.916645	+	0.0739992i
$447$	−6.65248	+	12.6752i	−0.314651	+	0.599518i
$448$	3.65416	+	3.50987i	0.172643	+	0.165826i
$449$	13.4540	−	31.5776i	0.634931	−	1.49024i	−0.222127	−	0.975018i	$-0.571300\pi$
$449$	13.4540	−	31.5776i	0.634931	−	1.49024i	0.857058	−	0.515220i	$-0.172290\pi$
$450$	6.80937	+	2.58245i	0.320997	+	0.121738i
$451$	−20.8122	−	3.38231i	−0.980007	−	0.159267i
$452$	16.6023	+	10.4987i	0.780906	+	0.493815i
$453$	10.1461	−	2.93886i	0.476707	−	0.138080i
$454$	6.94926	−	10.0677i	0.326145	−	0.472502i
$455$	25.1202	−	15.3245i	1.17765	−	0.718422i
$456$	−1.22639	−	1.77673i	−0.0574308	−	0.0832029i
$457$	27.5282	+	22.4761i	1.28772	+	1.05139i	0.995473	+	0.0950445i	$0.0302993\pi$
$457$	27.5282	+	22.4761i	1.28772	+	1.05139i	0.292244	+	0.956344i	$0.405598\pi$
$458$	−21.3729	+	26.1771i	−0.998692	+	1.22318i
$459$	0.576696	+	0.433359i	0.0269179	+	0.0202275i
$460$	2.50178	+	0.303771i	0.116646	+	0.0141634i
$461$	−4.75606	−	14.2461i	−0.221512	−	0.663508i	−0.999384	−	0.0350863i	$-0.988829\pi$
$461$	−4.75606	−	14.2461i	−0.221512	−	0.663508i	0.777873	−	0.628422i	$-0.216299\pi$
$462$	−0.914313	−	11.3258i	−0.0425377	−	0.526924i
$463$	2.12382	−	2.39729i	0.0987021	−	0.111412i	−0.697084	−	0.716990i	$-0.745520\pi$
$463$	2.12382	−	2.39729i	0.0987021	−	0.111412i	0.795786	+	0.605578i	$0.207058\pi$
$464$	16.4039	−	10.3732i	0.761533	−	0.481565i
$465$	−21.1014	+	8.99047i	−0.978555	+	0.416923i
$466$	0.554389	+	3.41129i	0.0256816	+	0.158025i
$467$	4.10051	−	3.63273i	0.189749	−	0.168103i	−0.562900	−	0.826525i	$-0.690314\pi$
$467$	4.10051	−	3.63273i	0.189749	−	0.168103i	0.752649	+	0.658422i	$0.228776\pi$
$468$	−1.24153	−	4.55977i	−0.0573899	−	0.210775i
$469$	−0.702015	−	0.621931i	−0.0324160	−	0.0287181i
$470$	2.31321	−	3.65804i	0.106700	−	0.168733i
$471$	4.30355	+	0.347418i	0.198297	+	0.0160082i
$472$	−2.18387	−	10.6973i	−0.100521	−	0.492384i
$473$	5.10272	+	20.7025i	0.234623	+	0.951904i
$474$	2.04707	−	12.5961i	0.0940250	−	0.578559i
$475$	3.68218	+	5.82290i	0.168950	+	0.267173i
$476$	−1.19516	−	2.27719i	−0.0547802	−	0.104375i
$477$	3.58192	−	12.3662i	0.164005	−	0.566211i
$478$	1.47745	−	7.23701i	0.0675768	−	0.331013i
$479$	−17.1845	+	0.692514i	−0.785182	+	0.0316418i	−0.429619	−	0.903010i	$-0.641352\pi$
$479$	−17.1845	+	0.692514i	−0.785182	+	0.0316418i	−0.355563	+	0.934652i	$0.615711\pi$
$480$	17.0392	−	8.94285i	0.777728	−	0.408183i
$481$	4.64634	+	1.02676i	0.211855	+	0.0468160i
$482$	−42.9843	−	22.5599i	−1.95788	−	1.02757i
$483$	−1.57479	−	0.747246i	−0.0716554	−	0.0340009i
$484$	3.75445	+	6.50290i	0.170657	+	0.295587i
$485$	19.0155	−	32.9359i	0.863451	−	1.49554i
$486$	−1.49744	+	1.03361i	−0.0679255	+	0.0468856i
$487$	−17.5223	+	23.3180i	−0.794013	+	1.05664i	0.202982	+	0.979182i	$0.434937\pi$
$487$	−17.5223	+	23.3180i	−0.794013	+	1.05664i	−0.996996	+	0.0774576i	$0.975320\pi$
$488$	−4.92785	−	2.84509i	−0.223073	−	0.128791i
$489$	−5.70315	+	0.692488i	−0.257906	+	0.0313154i
$490$	0.932658	+	1.96554i	0.0421332	+	0.0887939i
$491$	12.2835	+	12.7885i	0.554347	+	0.577136i	0.938128	−	0.346288i	$-0.112558\pi$
$491$	12.2835	+	12.7885i	0.554347	+	0.577136i	−0.383782	+	0.923424i	$0.625378\pi$
$492$	0.968604	−	11.9983i	0.0436680	−	0.540926i
$493$	−2.77232	+	0.683315i	−0.124859	+	0.0307750i
$494$	4.17384	−	10.4928i	0.187790	−	0.472092i
$495$	−6.68840	−	1.64854i	−0.300621	−	0.0740965i
$496$	−11.8703	+	35.5558i	−0.532990	+	1.59650i
$497$	2.88489	−	6.07977i	0.129405	−	0.272715i
$498$	4.67856	−	1.56193i	0.209651	−	0.0699918i
$499$	4.76209	+	3.28704i	0.213181	+	0.147148i	0.669870	−	0.742478i	$-0.266350\pi$
$499$	4.76209	+	3.28704i	0.213181	+	0.147148i	−0.456690	+	0.889626i	$0.650965\pi$
$500$	3.54414	−	1.68171i	0.158499	−	0.0752085i
$501$	22.4329	+	0.904014i	1.00223	+	0.0403884i
$502$	4.13717	−	16.7852i	0.184651	−	0.749159i
$503$	−24.9226	−	10.6185i	−1.11124	−	0.473457i	−0.243216	−	0.969972i	$-0.578202\pi$
$503$	−24.9226	−	10.6185i	−1.11124	−	0.473457i	−0.868028	+	0.496515i	$0.834613\pi$
$504$	−3.36732	+	0.547242i	−0.149992	+	0.0243761i
$505$	−54.4353	−	11.1131i	−2.42234	−	0.494524i
$506$	−2.67703			−0.119009
$507$	−8.54176	+	9.79991i	−0.379353	+	0.435229i
$508$	18.8902			0.838116
$509$	13.5472	+	2.76568i	0.600469	+	0.122587i	0.490638	−	0.871363i	$-0.336764\pi$
$509$	13.5472	+	2.76568i	0.600469	+	0.122587i	0.109831	+	0.993950i	$0.464969\pi$
$510$	−3.88722	+	0.631735i	−0.172129	+	0.0279737i
$511$	12.3450	+	5.25972i	0.546111	+	0.232676i
$512$	4.58260	−	18.5923i	0.202524	−	0.821673i
$513$	−1.71990	−	0.0693098i	−0.0759357	−	0.00306010i
$514$	−13.9849	+	6.63593i	−0.616849	+	0.292698i
$515$	2.72239	+	1.87913i	0.119963	+	0.0828045i
$516$	−11.5462	+	3.85467i	−0.508291	+	0.169692i
$517$	−0.780275	+	1.64440i	−0.0343165	+	0.0723204i
$518$	−2.06837	+	6.19553i	−0.0908790	+	0.272216i
$519$	−0.375166	−	0.0924701i	−0.0164680	−	0.00405899i
$520$	−11.9110	−	6.49813i	−0.522334	−	0.284962i
$521$	19.3567	−	4.77100i	0.848033	−	0.209021i	0.208727	−	0.977974i	$-0.433068\pi$
$521$	19.3567	−	4.77100i	0.848033	−	0.209021i	0.639306	+	0.768953i	$0.279222\pi$
$522$	0.579515	−	7.17858i	0.0253647	−	0.314198i
$523$	−5.28839	−	5.50580i	−0.231245	−	0.240752i	0.595463	−	0.803383i	$-0.296969\pi$
$523$	−5.28839	−	5.50580i	−0.231245	−	0.240752i	−0.826708	+	0.562631i	$0.809789\pi$
$524$	11.4226	+	24.0726i	0.498998	+	1.05162i
$525$	10.8074	−	1.31226i	0.471675	−	0.0572717i
$526$	−13.3502	−	7.70775i	−0.582097	−	0.336074i
$527$	3.31284	−	4.40859i	0.144310	−	0.192041i
$528$	−9.26495	+	6.39513i	−0.403205	+	0.278312i
$529$	11.2947	−	19.5629i	0.491072	−	0.850562i
$530$	35.1433	+	60.8699i	1.52653	+	2.64402i
$531$	−7.86454	−	3.73177i	−0.341292	−	0.161945i
$532$	5.43371	+	2.85183i	0.235581	+	0.123643i
$533$	−28.9398	+	16.0927i	−1.25352	+	0.697054i
$534$	−19.5450	+	10.2580i	−0.845794	+	0.443907i
$535$	19.9417	−	0.803625i	0.862157	−	0.0347437i
$536$	−0.0865037	+	0.423723i	−0.00373639	+	0.0183020i
$537$	0.329430	−	1.13732i	0.0142159	−	0.0490791i
$538$	22.0168	+	41.9495i	0.949210	+	1.80857i
$539$	−0.488995	−	0.773284i	−0.0210625	−	0.0333077i
$540$	0.630836	−	3.88169i	0.0271469	−	0.167041i
$541$	0.692777	+	2.81071i	0.0297848	+	0.120842i	0.983952	−	0.178431i	$-0.0571021\pi$
$541$	0.692777	+	2.81071i	0.0297848	+	0.120842i	−0.954168	+	0.299273i	$0.903256\pi$
$542$	6.94511	+	34.0194i	0.298318	+	1.46126i
$543$	−22.6458	−	1.82816i	−0.971824	−	0.0784538i
$544$	−2.47275	+	3.91034i	−0.106018	+	0.167655i
$545$	−19.2229	−	17.0300i	−0.823420	−	0.729487i
$546$	−12.1525	−	13.0668i	−0.520078	−	0.559209i
$547$	−15.4499	+	13.6874i	−0.660591	+	0.585232i	−0.925365	−	0.379078i	$-0.876241\pi$
$547$	−15.4499	+	13.6874i	−0.660591	+	0.585232i	0.264774	+	0.964311i	$0.414703\pi$
$548$	1.51048	+	9.29436i	0.0645246	+	0.397036i
$549$	−4.17380	+	1.77829i	−0.178134	+	0.0758956i
$550$	14.1316	−	8.93626i	0.602572	−	0.381043i
$551$	4.51794	−	5.09970i	0.192471	−	0.217255i
$552$	0.0646746	+	0.801139i	0.00275274	+	0.0340987i
$553$	−6.04108	−	18.0952i	−0.256893	−	0.769488i
$554$	−50.1760	−	6.09247i	−2.13178	−	0.258844i
$555$	3.16564	+	2.37882i	0.134374	+	0.100975i
$556$	−11.3744	+	13.9312i	−0.482384	+	0.590813i
$557$	−6.93443	−	5.66178i	−0.293821	−	0.239897i	0.474056	−	0.880495i	$-0.342789\pi$
$557$	−6.93443	−	5.66178i	−0.293821	−	0.239897i	−0.767877	+	0.640597i	$0.778687\pi$
$558$	7.90150	+	11.4473i	0.334497	+	0.484603i
$559$	26.4422	+	20.5445i	1.11839	+	0.868938i
$560$	22.7329	−	32.9343i	0.960639	−	1.39173i
$561$	1.59079	−	0.460779i	0.0671633	−	0.0194541i
$562$	37.7923	+	23.8984i	1.59417	+	1.00809i
$563$	21.8755	+	3.55511i	0.921942	+	0.149830i	0.602814	−	0.797882i	$-0.294046\pi$
$563$	21.8755	+	3.55511i	0.921942	+	0.149830i	0.319128	+	0.947712i	$0.396610\pi$
$564$	−0.971569	−	0.368468i	−0.0409104	−	0.0155153i
$565$	17.6256	−	41.3687i	0.741513	−	1.74040i
$566$	21.2040	+	20.3668i	0.891273	+	0.856079i
$567$	−1.26406	+	2.40846i	−0.0530854	+	0.101146i
$568$	−3.09295	+	0.249689i	−0.129777	+	0.0104767i
$569$	−2.78469	−	9.61385i	−0.116740	−	0.403034i	0.880771	−	0.473542i	$-0.157025\pi$
$569$	−2.78469	−	9.61385i	−0.116740	−	0.403034i	−0.997511	+	0.0705087i	$0.977538\pi$
$570$	6.77726	−	6.50965i	0.283868	−	0.272659i
$571$	−14.6477	−	38.6227i	−0.612986	−	1.61631i	−0.776749	−	0.629811i	$-0.783133\pi$
$571$	−14.6477	−	38.6227i	−0.612986	−	1.61631i	0.163763	−	0.986500i	$-0.447637\pi$
$572$	−10.0814	−	4.01023i	−0.421526	−	0.167676i
$573$	8.57481	−	22.6099i	0.358218	−	0.944542i
$574$	−17.8160	−	41.8157i	−0.743626	−	1.74535i
$575$	−0.103279	−	2.56284i	−0.00430703	−	0.106878i
$576$	−1.17810	−	1.44291i	−0.0490875	−	0.0601212i
$577$			20.3014i			0.845157i	0.906326	+	0.422578i	$0.138875\pi$
$577$			20.3014i			0.845157i	−0.906326	+	0.422578i	$0.861125\pi$
$578$	−23.2267	+	18.9640i	−0.966102	+	0.788798i
$579$	9.43039	+	2.73155i	0.391914	+	0.113519i
$580$	10.3220	+	11.6512i	0.428599	+	0.483789i
$581$	5.10777	−	5.31775i	0.211906	−	0.220617i
$582$	−21.8762	−	7.30333i	−0.906796	−	0.302733i
$583$	−17.7569	−	23.6302i	−0.735417	−	0.978662i
$584$	−0.745818	−	6.14237i	−0.0308622	−	0.254173i
$585$	−9.84706	+	4.47969i	−0.407126	+	0.185212i
$586$	0.179738	−	1.48027i	0.00742490	−	0.0611495i
$587$	−25.6650	+	14.8177i	−1.05931	+	0.611592i	−0.925241	−	0.379380i	$-0.876137\pi$
$587$	−25.6650	+	14.8177i	−1.05931	+	0.611592i	−0.134067	+	0.990972i	$0.542804\pi$
$588$	0.417565	−	0.313780i	0.0172201	−	0.0129401i
$589$	−0.529843	+	13.1479i	−0.0218318	+	0.541750i
$590$	44.4353	−	16.8521i	1.82937	−	0.693790i
$591$	−8.07539	+	1.64860i	−0.332177	+	0.0678145i
$592$	6.34059	−	1.29444i	0.260597	−	0.0532012i
$593$	26.4892	−	10.0460i	1.08778	−	0.412542i	0.255452	−	0.966822i	$-0.417776\pi$
$593$	26.4892	−	10.0460i	1.08778	−	0.412542i	0.832330	+	0.554280i	$0.187006\pi$
$594$	−0.168207	+	4.17403i	−0.00690164	+	0.171262i
$595$	−4.70652	+	3.53672i	−0.192949	+	0.144991i
$596$	−16.2488	+	9.38123i	−0.665575	+	0.384270i
$597$	1.67737	−	13.8144i	0.0686501	−	0.565384i
$598$	−3.29894	+	2.60611i	−0.134904	+	0.106572i
$599$	4.29777	+	35.3953i	0.175602	+	1.44621i	0.767939	+	0.640524i	$0.221283\pi$
$599$	4.29777	+	35.3953i	0.175602	+	1.44621i	−0.592336	+	0.805691i	$0.701794\pi$
$600$	−3.01571	−	4.01318i	−0.123116	−	0.163837i
$601$	−15.6027	−	5.20895i	−0.636448	−	0.212477i	−0.0199086	−	0.999802i	$-0.506338\pi$
$601$	−15.6027	−	5.20895i	−0.636448	−	0.212477i	−0.616539	+	0.787324i	$0.711466\pi$
$602$	−31.8401	+	33.1491i	−1.29771	+	1.35105i
$603$	0.228649	+	0.258092i	0.00931132	+	0.0105103i
$604$	13.2985	+	3.85195i	0.541107	+	0.156733i
$605$	13.3149	−	10.8713i	0.541327	−	0.441980i
$606$			33.6919i			1.36864i
$607$	−28.5532	−	34.9713i	−1.15894	−	1.41944i	−0.889806	−	0.456340i	$-0.849160\pi$
$607$	−28.5532	−	34.9713i	−1.15894	−	1.41944i	−0.269134	−	0.963103i	$-0.586737\pi$
$608$	−0.444524	−	11.0307i	−0.0180278	−	0.447356i
$609$	−4.21999	−	9.90467i	−0.171002	−	0.401358i
$610$	8.78292	−	23.1587i	0.355610	−	0.937667i
$611$	0.639288	+	2.78601i	0.0258628	+	0.112710i
$612$	0.335278	+	0.884056i	0.0135528	+	0.0357358i
$613$	5.54778	−	5.32871i	0.224073	−	0.215225i	−0.572278	−	0.820059i	$-0.693940\pi$
$613$	5.54778	−	5.32871i	0.224073	−	0.215225i	0.796351	+	0.604835i	$0.206761\pi$
$614$	4.82150	+	16.6457i	0.194580	+	0.671767i
$615$	−27.4663	+	2.21731i	−1.10755	+	0.0894106i
$616$	−3.63988	+	6.93521i	−0.146655	+	0.279428i
$617$	−12.5786	−	12.0819i	−0.506394	−	0.486398i	0.395434	−	0.918495i	$-0.370594\pi$
$617$	−12.5786	−	12.0819i	−0.506394	−	0.486398i	−0.901827	+	0.432097i	$0.857774\pi$
$618$	0.786298	−	1.84551i	0.0316295	−	0.0742373i
$619$	7.81132	+	2.96244i	0.313963	+	0.119071i	0.506553	−	0.862209i	$-0.330919\pi$
$619$	7.81132	+	2.96244i	0.313963	+	0.119071i	−0.192590	+	0.981279i	$0.561689\pi$
$620$	−29.6738	−	4.82246i	−1.19173	−	0.193675i
$621$	0.541627	+	0.342504i	0.0217347	+	0.0137442i
$622$	−20.5963	+	5.96578i	−0.825835	+	0.239206i
$623$	−18.7447	+	27.1564i	−0.750991	+	1.08800i
$624$	−5.19160	+	16.9003i	−0.207830	+	0.676553i
$625$	−16.4697	−	23.8604i	−0.658786	−	0.954417i
$626$	21.2114	+	17.3185i	0.847777	+	0.692188i
$627$	−2.49935	+	3.06115i	−0.0998146	+	0.122251i
$628$	4.52403	+	3.39959i	0.180528	+	0.135658i
$629$	−0.945093	−	0.114755i	−0.0376833	−	0.00457558i
$630$	−4.70237	−	14.0853i	−0.187347	−	0.561172i
$631$	1.13250	+	14.0285i	0.0450841	+	0.558466i	0.979388	+	0.201989i	$0.0647404\pi$
$631$	1.13250	+	14.0285i	0.0450841	+	0.558466i	−0.934304	+	0.356478i	$0.883978\pi$
$632$	−5.83317	+	6.58429i	−0.232031	+	0.261909i
$633$	−6.39362	+	4.04308i	−0.254124	+	0.160698i
$634$	42.7382	−	18.2091i	1.69735	−	0.723174i
$635$	−6.93667	−	42.6830i	−0.275273	−	1.69382i
$636$	12.6308	−	11.1899i	0.500843	−	0.443708i
$637$	−1.35539	−	0.476886i	−0.0537026	−	0.0188949i
$638$	−12.3764	−	10.9646i	−0.489988	−	0.434091i
$639$	−1.32230	+	2.09105i	−0.0523095	+	0.0827209i
$640$	−28.2255	−	2.27860i	−1.11571	−	0.0900694i
$641$	−1.29648	−	6.35059i	−0.0512080	−	0.250833i	0.946127	−	0.323797i	$-0.104959\pi$
$641$	−1.29648	−	6.35059i	−0.0512080	−	0.250833i	−0.997335	+	0.0729636i	$0.976754\pi$
$642$	−2.89644	−	11.7513i	−0.114314	−	0.463788i
$643$	−6.07386	+	37.3739i	−0.239529	+	1.47388i	0.536882	+	0.843657i	$0.319602\pi$
$643$	−6.07386	+	37.3739i	−0.239529	+	1.47388i	−0.776411	+	0.630227i	$0.782962\pi$
$644$	−1.22106	−	1.93096i	−0.0481167	−	0.0760904i
$645$	12.9496	+	24.6735i	0.509892	+	0.971518i
$646$	−0.628580	+	2.17011i	−0.0247311	+	0.0853818i
$647$	−2.76876	+	13.5623i	−0.108851	+	0.533189i	0.888398	+	0.459073i	$0.151819\pi$
$647$	−2.76876	+	13.5623i	−0.108851	+	0.533189i	−0.997250	+	0.0741157i	$0.976387\pi$
$648$	1.25320	−	0.0505022i	0.0492303	−	0.00198391i
$649$	−17.6964	+	9.28777i	−0.694643	+	0.364577i
$650$	8.71498	−	24.7694i	0.341830	−	0.971537i
$651$	18.4116	+	9.66315i	0.721608	+	0.378729i
$652$	−6.80296	−	3.22805i	−0.266425	−	0.126420i
$653$	22.9380	+	39.7298i	0.897634	+	1.55475i	0.830510	+	0.557003i	$0.188049\pi$
$653$	22.9380	+	39.7298i	0.897634	+	1.55475i	0.0671240	+	0.997745i	$0.478618\pi$
$654$	−7.78700	+	13.4875i	−0.304496	+	0.527402i
$655$	50.1984	−	34.6494i	1.96141	−	1.35387i
$656$	−27.0534	+	36.0015i	−1.05626	+	1.40562i
$657$	−4.27240	−	2.46667i	−0.166682	−	0.0962340i
$658$	−3.89500	+	0.472938i	−0.151843	+	0.0184371i
$659$	−21.8902	−	46.1326i	−0.852722	−	1.79707i	−0.520462	−	0.853885i	$-0.674240\pi$
$659$	−21.8902	−	46.1326i	−0.852722	−	1.79707i	−0.332260	−	0.943188i	$-0.607811\pi$
$660$	−6.25446	−	6.51159i	−0.243455	−	0.253463i
$661$	0.109086	−	1.35127i	0.00424295	−	0.0525584i	−0.994289	−	0.106718i	$-0.965966\pi$
$661$	0.109086	−	1.35127i	0.00424295	−	0.0525584i	0.998532	+	0.0541594i	$0.0172479\pi$
$662$	−4.98774	+	1.22937i	−0.193854	+	0.0477807i
$663$	1.51178	−	2.11647i	0.0587127	−	0.0821969i
$664$	−3.30114	−	0.813659i	−0.128109	−	0.0315761i
$665$	4.44850	−	13.3249i	0.172506	−	0.516717i
$666$	1.02943	−	2.16948i	0.0398897	−	0.0840658i
$667$	−2.40597	+	0.803230i	−0.0931595	+	0.0311012i
$668$	24.2175	+	16.7161i	0.937004	+	0.646767i
$669$	9.64326	−	4.57578i	0.372830	−	0.176910i
$670$	−1.88089	−	0.0757974i	−0.0726652	−	0.00292831i
$671$	−2.49272	+	10.1134i	−0.0962303	+	0.390422i
$672$	−16.0491	−	6.83788i	−0.619108	−	0.263777i
$673$	19.4856	−	3.16672i	0.751115	−	0.122068i	0.227211	−	0.973845i	$-0.427039\pi$
$673$	19.4856	−	3.16672i	0.751115	−	0.122068i	0.523904	+	0.851777i	$0.324475\pi$
$674$	−39.3558	−	8.03454i	−1.51593	−	0.309479i
$675$	−4.00247			−0.154055
$676$	−16.3275	+	4.87251i	−0.627979	+	0.187404i
$677$	40.4891			1.55612			0.778061	−	0.628188i	$-0.216203\pi$
$677$	40.4891			1.55612			0.778061	+	0.628188i	$0.216203\pi$
$678$	−26.7181	−	5.45454i	−1.02610	−	0.209480i
$679$	−34.0305	+	5.53050i	−1.30597	+	0.212241i
$680$	2.49742	+	1.06405i	0.0957717	+	0.0408045i
$681$	−1.60899	+	6.52791i	−0.0616565	+	0.250150i
$682$	31.9086	+	1.28587i	1.22184	+	0.0492386i
$683$	17.1947	−	8.15899i	0.657937	−	0.312195i	−0.0702944	−	0.997526i	$-0.522394\pi$
$683$	17.1947	−	8.15899i	0.657937	−	0.312195i	0.728231	+	0.685331i	$0.240343\pi$
$684$	−1.85673	−	1.28161i	−0.0709938	−	0.0490035i
$685$	20.4463	−	6.82598i	0.781213	−	0.260807i
$686$	−14.0062	+	29.5174i	−0.534758	+	1.12698i
$687$	5.88147	−	17.6172i	0.224392	−	0.672136i
$688$	44.2160	+	10.8983i	1.68572	+	0.415492i
$689$	−44.8862	−	11.8333i	−1.71003	−	0.450811i
$690$	−3.39687	+	0.837254i	−0.129317	+	0.0318737i
$691$	−1.80321	+	22.3368i	−0.0685974	+	0.849731i	0.867374	+	0.497656i	$0.165806\pi$
$691$	−1.80321	+	22.3368i	−0.0685974	+	0.849731i	−0.935972	+	0.352075i	$0.885476\pi$
$692$	−0.350826	−	0.365248i	−0.0133364	−	0.0138847i
$693$	2.67711	+	5.64189i	0.101695	+	0.214318i
$694$	−41.8146	+	5.07722i	−1.58726	+	0.192728i
$695$	35.6548	+	20.5853i	1.35246	+	0.780845i
$696$	−2.98230	+	3.96872i	−0.113044	+	0.150434i
$697$	5.45232	−	3.76346i	0.206521	−	0.142551i
$698$	26.1958	−	45.3725i	0.991527	−	1.71738i
$699$	−0.949708	−	1.64494i	−0.0359213	−	0.0622175i
$700$	12.8916	+	6.11712i	0.487255	+	0.231206i
$701$	4.56882	+	2.39790i	0.172562	+	0.0905674i	0.548793	−	0.835959i	$-0.315088\pi$
$701$	4.56882	+	2.39790i	0.172562	+	0.0905674i	−0.376231	+	0.926526i	$0.622780\pi$
$702$	3.85616	+	5.30745i	0.145541	+	0.200317i
$703$	2.01148	−	1.05571i	0.0758646	−	0.0398168i
$704$	−4.27321	+	0.172205i	−0.161053	+	0.00649020i
$705$	−0.475796	+	2.33060i	−0.0179195	+	0.0877756i
$706$	−1.09993	+	3.79739i	−0.0413963	+	0.142917i
$707$	23.4063	+	44.5970i	0.880285	+	1.67724i
$708$	−6.09803	−	9.64326i	−0.229178	−	0.362416i
$709$	5.29932	−	32.6080i	0.199020	−	1.22462i	−0.674663	−	0.738126i	$-0.735711\pi$
$709$	5.29932	−	32.6080i	0.199020	−	1.22462i	0.873683	−	0.486495i	$-0.161725\pi$
$710$	−3.23238	−	13.1143i	−0.121309	−	0.492170i
$711$	1.40289	+	6.87182i	0.0526125	+	0.257713i
$712$	15.1660	+	1.22433i	0.568370	+	0.0458835i
$713$	2.61829	−	4.14050i	0.0980559	−	0.155063i
$714$	2.67233	+	2.36747i	0.100009	+	0.0886005i
$715$	−5.35924	+	24.2520i	−0.200424	+	0.906973i
$716$	1.16165	−	1.02914i	0.0434131	−	0.0384606i
$717$	0.651180	+	4.00687i	0.0243188	+	0.149639i
$718$	8.09636	−	3.44954i	0.302154	−	0.128736i
$719$	20.4374	−	12.9238i	0.762185	−	0.481977i	−0.0959593	−	0.995385i	$-0.530592\pi$
$719$	20.4374	−	12.9238i	0.762185	−	0.481977i	0.858144	+	0.513409i	$0.171617\pi$
$720$	−9.75615	+	11.0124i	−0.363590	+	0.410408i
$721$	−0.241305	−	2.98910i	−0.00898667	−	0.111320i
$722$	9.24038	+	27.6783i	0.343892	+	1.03008i
$723$	26.4853	+	3.21590i	0.984999	+	0.119601i
$724$	−23.8060	−	17.8890i	−0.884743	−	0.664841i
$725$	10.0194	−	12.2715i	0.372111	−	0.455753i
$726$	−8.07450	−	6.59263i	−0.299673	−	0.244675i
$727$	−5.43760	−	7.87772i	−0.201669	−	0.292168i	0.709080	−	0.705128i	$-0.249110\pi$
$727$	−5.43760	−	7.87772i	−0.201669	−	0.292168i	−0.910749	+	0.412960i	$0.864495\pi$
$728$	2.26601	+	12.0898i	0.0839840	+	0.448077i
$729$	0.568065	−	0.822984i	0.0210394	−	0.0304809i
$730$	25.8694	−	7.49318i	0.957471	−	0.277335i
$731$	−5.66235	−	3.58065i	−0.209430	−	0.132435i
$732$	−5.86940	−	0.953871i	−0.216939	−	0.0352561i
$733$	−44.6184	−	16.9215i	−1.64802	−	0.625011i	−0.656424	−	0.754392i	$-0.727932\pi$
$733$	−44.6184	−	16.9215i	−1.64802	−	0.625011i	−0.991595	+	0.129381i	$0.958701\pi$
$734$	18.4759	−	43.3646i	0.681959	−	1.60062i
$735$	−0.862332	−	0.828281i	−0.0318076	−	0.0305516i
$736$	−1.91003	+	3.63926i	−0.0704047	+	0.134145i
$737$	0.789066	−	0.0637000i	0.0290656	−	0.00234642i
$738$	4.64915	+	16.0507i	0.171138	+	0.590836i
$739$	−19.8914	+	19.1060i	−0.731717	+	0.702824i	−0.962832	−	0.270103i	$-0.912942\pi$
$739$	−19.8914	+	19.1060i	−0.731717	+	0.702824i	0.231114	+	0.972927i	$0.425763\pi$
$740$	1.84043	+	4.85281i	0.0676555	+	0.178393i
$741$	−0.0999291	+	6.20543i	−0.00367099	+	0.227962i
$742$	22.5948	−	59.5775i	0.829480	−	2.18716i
$743$	17.3416	+	40.7022i	0.636201	+	1.49322i	0.855629	+	0.517589i	$0.173170\pi$
$743$	17.3416	+	40.7022i	0.636201	+	1.49322i	−0.219429	+	0.975629i	$0.570419\pi$
$744$	−0.386067	−	9.58016i	−0.0141539	−	0.351226i
$745$	27.1640	+	33.2698i	0.995210	+	1.21891i
$746$		−	50.8238i		−	1.86079i
$747$	−2.09980	+	1.71444i	−0.0768278	+	0.0627280i
$748$	2.08504	+	0.603939i	0.0762366	+	0.0220822i
$749$	−11.9978	−	13.5427i	−0.438389	−	0.494839i
$750$	−3.77246	+	3.92755i	−0.137751	+	0.143414i
$751$	44.5623	+	14.8771i	1.62610	+	0.542872i	0.976149	−	0.217103i	$-0.0696607\pi$
$751$	44.5623	+	14.8771i	1.62610	+	0.542872i	0.649952	+	0.759975i	$0.274789\pi$
$752$	2.33532	+	3.10774i	0.0851602	+	0.113328i
$753$	1.14523	+	9.43181i	0.0417345	+	0.343714i
$754$	−25.9257	−	1.46321i	−0.944158	−	0.0532871i
$755$	3.82028	−	31.4628i	0.139034	−	1.14505i
$756$	−3.08747	+	1.78255i	−0.112290	+	0.0648309i
$757$	−5.49280	+	4.12757i	−0.199639	+	0.150019i	−0.695861	−	0.718177i	$-0.744977\pi$
$757$	−5.49280	+	4.12757i	−0.199639	+	0.150019i	0.496221	+	0.868196i	$0.334720\pi$
$758$	1.56628	−	38.8669i	0.0568900	−	1.41171i
$759$	1.37567	−	0.521721i	0.0499335	−	0.0189373i
$760$	−6.34664	+	1.29568i	−0.230217	+	0.0469991i
$761$	8.21180	−	1.67645i	0.297678	−	0.0607713i	−0.0488655	−	0.998805i	$-0.515561\pi$
$761$	8.21180	−	1.67645i	0.297678	−	0.0607713i	0.346543	+	0.938034i	$0.387355\pi$
$762$	−24.5196	+	9.29906i	−0.888252	+	0.336870i
$763$	−0.937456	+	23.2627i	−0.0339382	+	0.842167i
$764$	25.3377	−	19.0401i	0.916687	−	0.688845i
$765$	1.87444	−	1.08221i	0.0677705	−	0.0391273i
$766$	0.472898	−	3.89466i	0.0170865	−	0.140720i
$767$	−12.7657	+	28.6730i	−0.460944	+	1.03532i
$768$	2.51896	+	20.7455i	0.0908953	+	0.748590i
$769$	6.93051	+	9.22283i	0.249920	+	0.332584i	0.906917	−	0.421310i	$-0.138430\pi$
$769$	6.93051	+	9.22283i	0.249920	+	0.332584i	−0.656996	+	0.753894i	$0.728173\pi$
$770$	−32.3381	−	10.7960i	−1.16538	−	0.389062i
$771$	5.89328	−	6.13555i	0.212241	−	0.220966i
$772$	8.53333	+	9.63214i	0.307121	+	0.346668i
$773$	−38.9618	−	11.2854i	−1.40136	−	0.405908i	−0.510378	−	0.859950i	$-0.670494\pi$
$773$	−38.9618	−	11.2854i	−1.40136	−	0.405908i	−0.890980	+	0.454042i	$0.849982\pi$
$774$	13.0895	−	10.6872i	0.470491	−	0.384144i
$775$			30.5972i			1.09908i
$776$	10.0543	+	12.3143i	0.360929	+	0.442058i
$777$	−0.144545	−	3.58684i	−0.00518552	−	0.128677i
$778$	15.0293	+	35.2751i	0.538826	+	1.26467i
$779$	−5.60572	+	14.7811i	−0.200846	+	0.529587i
$780$	−14.0465	−	1.93554i	−0.502946	−	0.0693034i
$781$	2.01421	+	5.31102i	0.0720739	+	0.190043i
$782$	0.606628	−	0.582674i	0.0216930	−	0.0208364i
$783$	1.10122	+	3.80185i	0.0393544	+	0.135867i
$784$	−1.94773	+	0.157237i	−0.0695619	+	0.00561562i
$785$	6.02022	−	11.4706i	0.214871	−	0.409402i
$786$	−26.6768	−	25.6234i	−0.951531	−	0.913958i
$787$	−1.87490	+	4.40054i	−0.0668328	+	0.156862i	−0.950046	−	0.312108i	$-0.898965\pi$
$787$	−1.87490	+	4.40054i	−0.0668328	+	0.156862i	0.883214	+	0.468971i	$0.155375\pi$
$788$	−10.1007	−	3.83068i	−0.359821	−	0.136462i
$789$	8.36252	+	1.35904i	0.297714	+	0.0483832i
$790$	−32.3618	−	20.4644i	−1.15138	−	0.728090i
$791$	−39.1553	+	11.3415i	−1.39220	+	0.403256i
$792$	1.63576	−	2.36980i	0.0581241	−	0.0842072i
$793$	6.77361	+	14.8895i	0.240538	+	0.528741i
$794$	33.7586	+	48.9078i	1.19805	+	1.73567i
$795$	−29.9222	−	24.4307i	−1.06123	−	0.866467i
$796$	11.5354	−	14.1283i	0.408862	−	0.500764i
$797$	−37.6923	−	28.3239i	−1.33513	−	1.00328i	−0.998089	−	0.0617930i	$-0.980318\pi$
$797$	−37.6923	−	28.3239i	−1.33513	−	1.00328i	−0.337039	−	0.941491i	$-0.609425\pi$
$798$	−8.45688	−	1.02685i	−0.299370	−	0.0363501i
$799$	−0.181100	−	0.542460i	−0.00640685	−	0.0191909i
$800$	−2.06559	−	25.5870i	−0.0730297	−	0.904635i
$801$	8.04457	−	9.08044i	0.284241	−	0.320842i
$802$	49.9358	−	31.5775i	1.76330	−	1.11504i
$803$	−10.4200	+	4.43954i	−0.367714	+	0.156668i
$804$	0.0724956	+	0.446083i	0.00255672	+	0.0157321i
$805$	−3.91469	+	3.46811i	−0.137975	+	0.122235i
$806$	40.5731	−	29.4786i	1.42913	−	1.03834i
$807$	−19.4894	−	17.2661i	−0.686059	−	0.607795i
$808$	12.4125	−	19.6288i	0.436670	−	0.690539i
$809$	13.1325	+	1.06017i	0.461715	+	0.0372735i	0.309136	−	0.951018i	$-0.399960\pi$
$809$	13.1325	+	1.06017i	0.461715	+	0.0372735i	0.152579	+	0.988291i	$0.451242\pi$
$810$	1.09201	+	5.34901i	0.0383693	+	0.187945i
$811$	3.99009	+	16.1884i	0.140111	+	0.568453i	0.998465	+	0.0553944i	$0.0176416\pi$
$811$	3.99009	+	16.1884i	0.140111	+	0.568453i	−0.858353	+	0.513059i	$0.828512\pi$
$812$	2.26359	−	13.9284i	0.0794364	−	0.488792i
$813$	−10.1989	−	16.1283i	−0.357692	−	0.565644i
$814$	−2.56209	−	4.88166i	−0.0898013	−	0.171102i
$815$	−4.79577	+	16.5569i	−0.167989	+	0.579964i
$816$	0.707537	−	3.46575i	0.0247687	−	0.121325i
$817$	15.9730	−	0.643691i	0.558825	−	0.0225199i
$818$	43.8966	−	23.0387i	1.53481	−	0.805529i
$819$	8.79145	+	4.34638i	0.307198	+	0.151875i
$820$	−31.9800	−	16.7844i	−1.11679	−	0.586137i
$821$	29.7509	+	14.1170i	1.03831	+	0.492686i	0.870002	−	0.493048i	$-0.164117\pi$
$821$	29.7509	+	14.1170i	1.03831	+	0.492686i	0.168311	+	0.985734i	$0.446169\pi$
$822$	−6.53596	−	11.3206i	−0.227968	−	0.394852i
$823$	24.3324	−	42.1449i	0.848174	−	1.46908i	−0.0346628	−	0.999399i	$-0.511036\pi$
$823$	24.3324	−	42.1449i	0.848174	−	1.46908i	0.882836	−	0.469681i	$-0.155631\pi$
$824$	−1.13800	+	0.785505i	−0.0396441	+	0.0273644i
$825$	−5.52033	+	7.34622i	−0.192193	+	0.255763i
$826$	−37.3105	−	21.5412i	−1.29820	−	0.749515i
$827$	−11.5878	+	1.40702i	−0.402948	+	0.0489268i	−0.319502	−	0.947586i	$-0.603516\pi$
$827$	−11.5878	+	1.40702i	−0.402948	+	0.0489268i	−0.0834460	+	0.996512i	$0.526593\pi$
$828$	0.360075	+	0.758841i	0.0125135	+	0.0263716i
$829$	−0.545831	−	0.568270i	−0.0189575	−	0.0197368i	0.711656	−	0.702528i	$-0.247945\pi$
$829$	−0.545831	−	0.568270i	−0.0189575	−	0.0197368i	−0.730614	+	0.682791i	$0.760766\pi$
$830$	1.19084	−	14.7512i	0.0413347	−	0.512023i
$831$	26.9717	−	6.64792i	0.935638	−	0.230614i
$832$	−5.09829	+	4.37221i	−0.176751	+	0.151579i
$833$	0.279119	+	0.0687967i	0.00967090	+	0.00238366i
$834$	7.90624	−	23.6821i	0.273771	−	0.820043i
$835$	28.8778	−	60.8587i	0.999358	−	2.10610i
$836$	−4.91314	+	1.64025i	−0.169925	+	0.0567292i
$837$	−6.29135	−	4.34261i	−0.217461	−	0.150102i
$838$	−29.6124	+	14.0512i	−1.02294	+	0.485392i
$839$	−36.3416	−	1.46452i	−1.25465	−	0.0505607i	−0.595985	−	0.802996i	$-0.703238\pi$
$839$	−36.3416	−	1.46452i	−1.25465	−	0.0505607i	−0.658667	+	0.752435i	$0.728879\pi$
$840$	−2.44961	+	9.93845i	−0.0845195	+	0.342909i
$841$	12.2663	+	5.22617i	0.422975	+	0.180213i
$842$	−9.06243	+	1.47279i	−0.312312	+	0.0507556i
$843$	−24.0781	−	4.91558i	−0.829294	−	0.169302i
$844$	−9.91501			−0.341289
$845$	17.0052	+	35.1033i	0.584998	+	1.20759i
$846$	1.44249			0.0495939
$847$	−15.2680	−	3.11698i	−0.524614	−	0.107101i
$848$	−62.3124	+	10.1267i	−2.13982	+	0.347754i
$849$	−14.8655	−	6.33361i	−0.510184	−	0.217369i
$850$	−1.25724	+	5.10083i	−0.0431230	+	0.174957i
$851$	−0.845058	−	0.0340547i	−0.0289682	−	0.00116738i
$852$	−2.92965	+	1.39014i	−0.100368	+	0.0476253i
$853$	−9.81580	−	6.77536i	−0.336086	−	0.231984i	0.388053	−	0.921637i	$-0.373148\pi$
$853$	−9.81580	−	6.77536i	−0.336086	−	0.231984i	−0.724140	+	0.689653i	$0.757763\pi$
$854$	−21.2980	+	7.11033i	−0.728803	+	0.243310i
$855$	−2.21403	+	4.66597i	−0.0757183	+	0.159573i
$856$	−2.64187	+	7.91336i	−0.0902972	+	0.270473i
$857$	5.69749	+	1.40430i	0.194622	+	0.0479701i	0.335422	−	0.942068i	$-0.391121\pi$
$857$	5.69749	+	1.40430i	0.194622	+	0.0479701i	−0.140799	+	0.990038i	$0.544967\pi$
$858$	15.0599	+	0.242517i	0.514137	+	0.00827941i
$859$	−21.2538	+	5.23859i	−0.725170	+	0.178738i	−0.584587	−	0.811331i	$-0.698744\pi$
$859$	−21.2538	+	5.23859i	−0.725170	+	0.178738i	−0.140582	+	0.990069i	$0.544897\pi$
$860$	−2.93887	+	36.4044i	−0.100214	+	1.24138i
$861$	17.3046	+	18.0160i	0.589741	+	0.613985i
$862$	2.08146	+	4.38658i	0.0708947	+	0.149407i
$863$	1.68907	−	0.205091i	0.0574967	−	0.00698136i	−0.0917378	−	0.995783i	$-0.529242\pi$
$863$	1.68907	−	0.205091i	0.0574967	−	0.00698136i	0.149234	+	0.988802i	$0.452319\pi$
$864$	5.55432	+	3.20679i	0.188962	+	0.109097i
$865$	−0.696465	+	0.926827i	−0.0236805	+	0.0315131i
$866$	38.7440	−	26.7431i	1.31657	−	0.908766i
$867$	8.23981	−	14.2718i	0.279839	−	0.484695i
$868$	13.6268	+	23.6024i	0.462525	+	0.801117i
$869$	14.5476	+	6.90291i	0.493493	+	0.234165i
$870$	−19.1336	−	10.0421i	−0.648691	−	0.340459i
$871$	0.910363	−	0.846660i	0.0308465	−	0.0286880i
$872$	9.50562	−	4.98893i	0.321901	−	0.168947i
$873$	12.6650	−	0.510382i	0.428645	−	0.0172738i
$874$	−0.401465	+	1.96651i	−0.0135798	+	0.0665181i
$875$	−2.26497	+	7.81957i	−0.0765698	+	0.264350i
$876$	−3.00494	−	5.72544i	−0.101528	−	0.193445i
$877$	10.3435	+	16.3569i	0.349275	+	0.552334i	0.973435	−	0.228962i	$-0.0735332\pi$
$877$	10.3435	+	16.3569i	0.349275	+	0.552334i	−0.624160	+	0.781296i	$0.714559\pi$
$878$	−3.82380	+	23.5288i	−0.129047	+	0.794057i
$879$	0.196125	+	0.795708i	0.00661512	+	0.0268386i
$880$	6.75645	+	33.0953i	0.227760	+	1.11564i
$881$	50.8460	+	4.10471i	1.71305	+	0.138291i	0.897678	−	0.440652i	$-0.145253\pi$
$881$	50.8460	+	4.10471i	1.71305	+	0.138291i	0.815368	+	0.578943i	$0.196535\pi$
$882$	−0.387539	+	0.612844i	−0.0130491	+	0.0206355i
$883$	−27.8002	−	24.6288i	−0.935550	−	0.828825i	0.0499059	−	0.998754i	$-0.484108\pi$
$883$	−27.8002	−	24.6288i	−0.935550	−	0.828825i	−0.985456	+	0.169929i	$0.945646\pi$
$884$	3.15736	−	1.28556i	0.106193	−	0.0432380i
$885$	−19.5501	+	17.3198i	−0.657168	+	0.582200i
$886$	−10.4089	−	64.0484i	−0.349693	−	2.15175i
$887$	−13.3378	+	5.68269i	−0.447838	+	0.190806i	−0.604098	−	0.796910i	$-0.706466\pi$
$887$	−13.3378	+	5.68269i	−0.447838	+	0.190806i	0.156260	+	0.987716i	$0.450056\pi$
$888$	−1.39901	+	0.884678i	−0.0469476	+	0.0296879i
$889$	−25.9957	+	29.3430i	−0.871867	+	0.984134i
$890$	5.32923	+	66.0144i	0.178636	+	2.21281i
$891$	−0.727030	−	2.17772i	−0.0243564	−	0.0729564i
$892$	13.8881	+	1.68632i	0.465007	+	0.0564621i
$893$	1.09093	+	0.819783i	0.0365067	+	0.0274330i
$894$	16.4730	−	20.1757i	0.550938	−	0.674776i
$895$	−2.75194	−	2.24689i	−0.0919874	−	0.0751053i
$896$	14.5828	+	21.1268i	0.487177	+	0.705798i
$897$	1.18735	−	1.98214i	0.0396445	−	0.0661819i
$898$	−35.4779	+	51.3986i	−1.18391	+	1.71519i
$899$	29.0635	−	8.41835i	0.969322	−	0.280768i
$900$	−4.43388	−	2.80381i	−0.147796	−	0.0934604i
$901$	9.16707	+	1.48979i	0.305399	+	0.0496322i
$902$	35.8721	+	13.6045i	1.19441	+	0.452980i
$903$	9.90156	−	23.2398i	0.329503	−	0.773373i
$904$	13.5564	+	13.0211i	0.450878	+	0.433074i
$905$	−31.6791	+	60.3596i	−1.05305	+	2.00642i
$906$	−19.1577	+	1.54657i	−0.636473	+	0.0513814i
$907$	4.91552	+	16.9703i	0.163217	+	0.563491i	0.999876	+	0.0157662i	$0.00501876\pi$
$907$	4.91552	+	16.9703i	0.163217	+	0.563491i	−0.836659	+	0.547725i	$0.815494\pi$
$908$	−6.35535	+	6.10439i	−0.210910	+	0.202581i
$909$	−6.56616	−	17.3135i	−0.217786	−	0.574254i
$910$	−50.3606	+	18.1773i	−1.66944	+	0.602571i
$911$	−15.7447	+	41.5155i	−0.521646	+	1.37547i	0.372641	+	0.927976i	$0.378452\pi$
$911$	−15.7447	+	41.5155i	−0.521646	+	1.37547i	−0.894287	+	0.447493i	$0.852317\pi$
$912$	3.30833	+	7.76495i	0.109550	+	0.257123i
$913$	0.250602	+	6.21862i	0.00829371	+	0.205806i
$914$	−40.8960	−	50.0885i	−1.35272	−	1.65678i
$915$			13.6124i			0.450012i
$916$	18.8566	−	15.3959i	0.623039	−	0.508695i
$917$	−53.1123	−	15.3842i	−1.75392	−	0.508030i
$918$	−0.870388	−	0.982465i	−0.0287271	−	0.0324262i
$919$	23.1263	−	24.0770i	0.762867	−	0.794228i	−0.220591	−	0.975366i	$-0.570799\pi$
$919$	23.1263	−	24.0770i	0.762867	−	0.794228i	0.983458	+	0.181138i	$0.0579781\pi$
$920$	2.28746	+	0.763666i	0.0754153	+	0.0251773i
$921$	−5.72172	−	7.61422i	−0.188537	−	0.250897i
$922$	3.29398	+	27.1284i	0.108482	+	0.893426i
$923$	7.65245	+	4.58399i	0.251883	+	0.150884i
$924$	−0.986598	+	8.12536i	−0.0324567	+	0.267305i
$925$	4.57459	−	2.64114i	0.150412	−	0.0868401i
$926$	−4.65875	+	3.50083i	−0.153096	+	0.115044i
$927$	−0.0443932	+	1.10161i	−0.00145806	+	0.0361815i
$928$	−23.7361	+	9.00192i	−0.779176	+	0.295503i
$929$	26.0373	−	5.31556i	0.854257	−	0.174398i	0.247110	−	0.968987i	$-0.420519\pi$
$929$	26.0373	−	5.31556i	0.854257	−	0.174398i	0.607147	+	0.794590i	$0.292314\pi$
$930$	40.8908	−	8.34793i	1.34086	−	0.273739i
$931$	−0.641375	+	0.243242i	−0.0210202	+	0.00797192i
$932$	0.100244	−	2.48753i	0.00328360	−	0.0814818i
$933$	9.42131	−	7.07965i	0.308440	−	0.231777i
$934$	−8.63236	+	4.98390i	−0.282460	+	0.163078i
$935$	0.598974	−	4.93300i	0.0195885	−	0.161326i
$936$	−0.291257	−	4.51275i	−0.00952005	−	0.147504i
$937$	−0.743853	−	6.12618i	−0.0243006	−	0.200133i	0.975502	−	0.219989i	$-0.0706023\pi$
$937$	−0.743853	−	6.12618i	−0.0243006	−	0.200133i	−0.999803	+	0.0198560i	$0.993679\pi$
$938$	1.02517	+	1.36425i	0.0334730	+	0.0445444i
$939$	−14.2752	−	4.76577i	−0.465854	−	0.155525i
$940$	−2.15971	+	2.24850i	−0.0704421	+	0.0733380i
$941$	−22.7613	−	25.6922i	−0.741996	−	0.837541i	0.249405	−	0.968399i	$-0.419765\pi$
$941$	−22.7613	−	25.6922i	−0.741996	−	0.837541i	−0.991401	+	0.130859i	$0.958227\pi$
$942$	−7.54575	−	2.18565i	−0.245854	−	0.0712124i
$943$	4.55886	−	3.72219i	0.148457	−	0.121211i
$944$			42.6847i			1.38927i
$945$	5.16150	+	6.32169i	0.167904	+	0.205645i
$946$	−1.56217	−	38.7648i	−0.0507905	−	1.26035i
$947$	−3.00348	−	7.04943i	−0.0976000	−	0.229076i	0.864022	−	0.503455i	$-0.167938\pi$
$947$	−3.00348	−	7.04943i	−0.0976000	−	0.229076i	−0.961622	+	0.274379i	$0.911528\pi$
$948$	−3.25975	+	8.59524i	−0.105872	+	0.279160i
$949$	−8.51875	+	15.6148i	−0.276530	+	0.506879i
$950$	−4.44518	−	11.7210i	−0.144221	−	0.380279i
$951$	−18.4135	+	17.6864i	−0.597099	+	0.573521i
$952$	−0.684682	−	2.36380i	−0.0221907	−	0.0766111i
$953$	−27.1343	+	2.19051i	−0.878966	+	0.0709575i	−0.511706	−	0.859161i	$-0.670986\pi$
$953$	−27.1343	+	2.19051i	−0.878966	+	0.0709575i	−0.367260	+	0.930118i	$0.619704\pi$
$954$	−10.8864	+	20.7424i	−0.352461	+	0.671558i
$955$	−52.3260	−	50.2598i	−1.69323	−	1.62637i
$956$	−2.08553	+	4.89491i	−0.0674508	+	0.158313i
$957$	8.49683	+	3.22242i	0.274664	+	0.104166i
$958$	30.8880	+	5.01978i	0.997944	+	0.162182i
$959$	−16.5161	−	10.4441i	−0.533331	−	0.337258i
$960$	−5.36840	+	1.55498i	−0.173265	+	0.0501867i
$961$	−15.5873	+	22.5821i	−0.502816	+	0.728455i
$962$	−7.90962	−	3.52151i	−0.255016	−	0.113538i
$963$	3.77861	+	5.47427i	0.121764	+	0.176406i
$964$	27.0872	+	22.1160i	0.872420	+	0.712309i
$965$	18.6307	−	22.8184i	0.599742	−	0.734551i
$966$	2.53551	+	1.90531i	0.0815786	+	0.0613023i
$967$	−15.1727	−	1.84230i	−0.487922	−	0.0592445i	−0.127121	−	0.991887i	$-0.540574\pi$
$967$	−15.1727	−	1.84230i	−0.487922	−	0.0592445i	−0.360801	+	0.932643i	$0.617497\pi$
$968$	2.27537	+	6.81558i	0.0731333	+	0.219061i
$969$	−0.0999153	−	1.23767i	−0.00320974	−	0.0397598i
$970$	−45.8872	+	51.7960i	−1.47335	+	1.66307i
$971$	−13.5634	+	8.57696i	−0.435270	+	0.275248i	−0.734078	−	0.679065i	$-0.762385\pi$
$971$	−13.5634	+	8.57696i	−0.435270	+	0.275248i	0.298808	+	0.954313i	$0.403411\pi$
$972$	1.20581	−	0.513748i	0.0386764	−	0.0164785i
$973$	−5.98705	−	36.8398i	−0.191936	−	1.18103i
$974$	39.7248	−	35.1931i	1.27286	−	1.12766i
$975$	0.348835	+	14.4269i	0.0111716	+	0.462031i
$976$	16.6516	+	14.7520i	0.533004	+	0.472200i
$977$	4.63193	−	7.32482i	0.148189	−	0.234342i	−0.762935	−	0.646476i	$-0.776242\pi$
$977$	4.63193	−	7.32482i	0.148189	−	0.234342i	0.911123	+	0.412134i	$0.135217\pi$
$978$	10.4194	+	0.841140i	0.333175	+	0.0268967i
$979$	−5.57112	−	27.2892i	−0.178054	−	0.872165i
$980$	−0.375050	−	1.52164i	−0.0119805	−	0.0486069i
$981$	1.37302	−	8.44851i	0.0438370	−	0.269740i
$982$	−17.2441	−	27.2694i	−0.550282	−	0.870201i
$983$	−3.54823	−	6.76060i	−0.113171	−	0.215630i	0.822282	−	0.569080i	$-0.192701\pi$
$983$	−3.54823	−	6.76060i	−0.113171	−	0.215630i	−0.935453	+	0.353451i	$0.885008\pi$
$984$	3.20470	−	11.0639i	0.102162	−	0.352704i
$985$	−4.94649	+	24.2295i	−0.157608	+	0.772016i
$986$	5.19107	−	0.209193i	0.165317	−	0.00666206i
$987$	1.90938	−	1.00212i	0.0607763	−	0.0318979i
$988$	−4.45773	+	6.80428i	−0.141819	+	0.216473i
$989$	−5.26982	−	2.76581i	−0.167570	−	0.0879477i
$990$	11.3238	+	5.37322i	0.359894	+	0.170772i
$991$	−24.8036	−	42.9610i	−0.787911	−	1.36470i	−0.927245	−	0.374456i	$-0.877829\pi$
$991$	−24.8036	−	42.9610i	−0.787911	−	1.36470i	0.139334	−	0.990245i	$-0.455504\pi$
$992$	24.5145	−	42.4604i	0.778336	−	1.34812i
$993$	2.32350	−	1.60379i	0.0737340	−	0.0508949i
$994$	−7.35581	+	9.78881i	−0.233312	+	0.310482i
$995$	−36.1594	−	20.8766i	−1.14633	−	0.661833i
$996$	−3.52713	+	0.428271i	−0.111761	+	0.0135703i
$997$	−22.1949	−	46.7747i	−0.702919	−	1.48137i	−0.868768	−	0.495219i	$-0.835088\pi$
$997$	−22.1949	−	46.7747i	−0.702919	−	1.48137i	0.165849	−	0.986151i	$-0.446964\pi$
$998$	−7.29334	−	7.59317i	−0.230867	−	0.240358i
$999$	−0.106196	+	1.31547i	−0.00335989	+	0.0416198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.10.4	✓	336
169.17	even	78	inner	507.2.t.a.355.4	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.10.4	✓	336	1.1	even	1	trivial
507.2.t.a.355.4	yes	336	169.17	even	78	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78276 - 0.363953i) q^{2} +(0.987050 - 0.160411i) q^{3} +(1.20581 + 0.513748i) q^{4} +(0.718046 - 2.91323i) q^{5} +(-1.81806 - 0.0732651i) q^{6} +(-2.45740 + 1.16605i) q^{7} +(1.03220 + 0.712476i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})\)	\(q+(-1.78276 - 0.363953i) q^{2} +(0.987050 - 0.160411i) q^{3} +(1.20581 + 0.513748i) q^{4} +(0.718046 - 2.91323i) q^{5} +(-1.81806 - 0.0732651i) q^{6} +(-2.45740 + 1.16605i) q^{7} +(1.03220 + 0.712476i) q^{8} +(0.948536 - 0.316668i) q^{9} +(-2.34038 + 4.93225i) q^{10} +(0.727030 - 2.17772i) q^{11} +(1.27261 + 0.313669i) q^{12} +(-1.22410 - 3.39140i) q^{13} +(4.80535 - 1.18441i) q^{14} +(0.241433 - 2.99068i) q^{15} +(-3.39675 - 3.53639i) q^{16} +(0.309247 + 0.651725i) q^{17} +(-1.80626 + 0.219320i) q^{18} +(-1.49069 - 0.860650i) q^{19} +(2.36249 - 3.14390i) q^{20} +(-2.23853 + 1.54515i) q^{21} +(-2.08871 + 3.61775i) q^{22} +(0.320417 + 0.554979i) q^{23} +(1.13312 + 0.537673i) q^{24} +(-3.54401 - 1.86004i) q^{25} +(0.947964 + 6.49156i) q^{26} +(0.885456 - 0.464723i) q^{27} +(-3.56222 + 0.143552i) q^{28} +(-0.791728 + 3.87814i) q^{29} +(-1.51888 + 5.24380i) q^{30} +(-3.55260 - 6.76892i) q^{31} +(3.42784 + 5.42070i) q^{32} +(0.368284 - 2.26614i) q^{33} +(-0.314116 - 1.27442i) q^{34} +(1.63245 + 7.99625i) q^{35} +(1.30644 + 0.105467i) q^{36} +(-0.705363 + 1.11544i) q^{37} +(2.34431 + 2.07687i) q^{38} +(-1.75227 - 3.15112i) q^{39} +(2.81677 - 2.49544i) q^{40} +(-1.47321 - 9.06503i) q^{41} +(4.55313 - 1.93991i) q^{42} +(-7.84941 + 4.96367i) q^{43} +(1.99546 - 2.25241i) q^{44} +(-0.241433 - 2.99068i) q^{45} +(-0.369241 - 1.10601i) q^{46} +(-0.787002 - 0.0955593i) q^{47} +(-3.92004 - 2.94572i) q^{48} +(0.252034 - 0.308686i) q^{49} +(5.64116 + 4.60586i) q^{50} +(0.409786 + 0.593678i) q^{51} +(0.266293 - 4.71826i) q^{52} +(7.31357 - 10.5955i) q^{53} +(-1.74769 + 0.506225i) q^{54} +(-5.82215 - 3.68170i) q^{55} +(-3.36732 - 0.547242i) q^{56} +(-1.60944 - 0.610382i) q^{57} +(2.82292 - 6.62563i) q^{58} +(-6.27807 - 6.03017i) q^{59} +(1.82758 - 3.48216i) q^{60} +(-4.52213 + 0.365064i) q^{61} +(3.86987 + 13.3603i) q^{62} +(-1.96168 + 1.88422i) q^{63} +(-0.660547 - 1.74172i) q^{64} +(-10.7589 + 1.13090i) q^{65} +(-1.48133 + 3.90595i) q^{66} +(0.135153 + 0.317215i) q^{67} +(0.0380714 + 0.944731i) q^{68} +(0.405293 + 0.496394i) q^{69} -14.8495i q^{70} +(-1.91642 + 1.56471i) q^{71} +(1.20470 + 0.348945i) q^{72} +(-3.27141 - 3.69266i) q^{73} +(1.66346 - 1.73185i) q^{74} +(-3.79649 - 1.26746i) q^{75} +(-1.35533 - 1.80362i) q^{76} +(0.752730 + 6.19929i) q^{77} +(1.97701 + 6.25543i) q^{78} +(-0.845391 + 6.96242i) q^{79} +(-12.7413 + 7.35622i) q^{80} +(0.799443 - 0.600742i) q^{81} +(-0.672864 + 16.6969i) q^{82} +(-2.53465 + 0.961265i) q^{83} +(-3.49306 + 0.713113i) q^{84} +(2.12067 - 0.432939i) q^{85} +(15.8001 - 5.99221i) q^{86} +(-0.159378 + 3.95492i) q^{87} +(2.30201 - 1.72985i) q^{88} +(10.5060 - 6.06567i) q^{89} +(-0.658051 + 5.41954i) q^{90} +(6.96265 + 6.90667i) q^{91} +(0.101243 + 0.833813i) q^{92} +(-4.59241 - 6.11139i) q^{93} +(1.36826 + 0.456791i) q^{94} +(-3.57765 + 3.72473i) q^{95} +(4.25299 + 4.80063i) q^{96} +(12.1748 + 3.52648i) q^{97} +(-0.561663 + 0.458584i) q^{98} -2.29587i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

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Database

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