LMFDB - Embedded newform 840.2.dc.e.53.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(53,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 6, 9, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dc (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [704,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$704$
Relative dimension:	$176$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.6
Character	$\chi$	$=$	840.53
Dual form			840.2.dc.e.317.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40478 - 0.163037i) q^{2} +(0.0253219 - 1.73187i) q^{3} +(1.94684 + 0.458064i) q^{4} +(-1.11326 - 1.93924i) q^{5} +(-0.317930 + 2.42877i) q^{6} +(0.130595 + 2.64253i) q^{7} +(-2.66021 - 0.960888i) q^{8} +(-2.99872 - 0.0877081i) q^{9} +(1.24772 + 2.90572i) q^{10} +(-1.45101 + 2.51322i) q^{11} +(0.842603 - 3.36006i) q^{12} +(-1.13395 + 1.13395i) q^{13} +(0.247372 - 3.73347i) q^{14} +(-3.38669 + 1.87891i) q^{15} +(3.58035 + 1.78355i) q^{16} +(5.80269 - 1.55483i) q^{17} +(4.19825 + 0.612113i) q^{18} +(4.22157 + 7.31197i) q^{19} +(-1.27904 - 4.28533i) q^{20} +(4.57981 - 0.159259i) q^{21} +(2.44811 - 3.29397i) q^{22} +(-0.212513 - 0.0569428i) q^{23} +(-1.73149 + 4.58279i) q^{24} +(-2.52130 + 4.31776i) q^{25} +(1.77783 - 1.40808i) q^{26} +(-0.227832 + 5.19116i) q^{27} +(-0.956199 + 5.20439i) q^{28} +5.64627i q^{29} +(5.06391 - 2.08731i) q^{30} +(3.40485 - 5.89737i) q^{31} +(-4.73884 - 3.08924i) q^{32} +(4.31582 + 2.57659i) q^{33} +(-8.40502 + 1.23814i) q^{34} +(4.97911 - 3.19508i) q^{35} +(-5.79784 - 1.54436i) q^{36} +(1.79632 - 6.70395i) q^{37} +(-4.73827 - 10.9600i) q^{38} +(1.93514 + 1.99256i) q^{39} +(1.09811 + 6.22850i) q^{40} +4.91810i q^{41} +(-6.45961 - 0.522953i) q^{42} +(-0.826434 + 0.826434i) q^{43} +(-3.97610 + 4.22818i) q^{44} +(3.16827 + 5.91287i) q^{45} +(0.289251 + 0.114640i) q^{46} +(1.31230 - 4.89758i) q^{47} +(3.17953 - 6.15553i) q^{48} +(-6.96589 + 0.690202i) q^{49} +(4.24584 - 5.65445i) q^{50} +(-2.54581 - 10.0889i) q^{51} +(-2.72704 + 1.68820i) q^{52} +(-6.91130 + 1.85188i) q^{53} +(1.16641 - 7.25531i) q^{54} +(6.48910 + 0.0159840i) q^{55} +(2.19176 - 7.15515i) q^{56} +(12.7703 - 7.12604i) q^{57} +(0.920551 - 7.93179i) q^{58} +(0.222735 + 0.128596i) q^{59} +(-7.45400 + 2.10662i) q^{60} +(0.0940230 - 0.0542842i) q^{61} +(-5.74457 + 7.72942i) q^{62} +(-0.159847 - 7.93564i) q^{63} +(6.15339 + 5.11232i) q^{64} +(3.46139 + 0.936620i) q^{65} +(-5.64272 - 4.32320i) q^{66} +(14.3124 - 3.83501i) q^{67} +(12.0091 - 0.368991i) q^{68} +(-0.103998 + 0.366603i) q^{69} +(-7.51549 + 3.67661i) q^{70} +12.8900i q^{71} +(7.89293 + 3.11475i) q^{72} +(0.272865 - 0.0731140i) q^{73} +(-3.61643 + 9.12474i) q^{74} +(7.41393 + 4.47589i) q^{75} +(4.86936 + 16.1690i) q^{76} +(-6.83075 - 3.50612i) q^{77} +(-2.39359 - 3.11462i) q^{78} +(-0.639229 + 0.369059i) q^{79} +(-0.527132 - 8.92873i) q^{80} +(8.98461 + 0.526024i) q^{81} +(0.801832 - 6.90886i) q^{82} +(2.53311 + 2.53311i) q^{83} +(8.98909 + 1.78779i) q^{84} +(-9.47509 - 9.52188i) q^{85} +(1.29570 - 1.02622i) q^{86} +(9.77857 + 0.142974i) q^{87} +(6.27491 - 5.29143i) q^{88} +(0.894453 + 1.54924i) q^{89} +(-3.48671 - 8.82286i) q^{90} +(-3.14458 - 2.84841i) q^{91} +(-0.387645 - 0.208203i) q^{92} +(-10.1272 - 6.04607i) q^{93} +(-2.64199 + 6.66609i) q^{94} +(9.47996 - 16.3268i) q^{95} +(-5.47014 + 8.12881i) q^{96} +(-7.84637 + 7.84637i) q^{97} +(9.89810 + 0.166114i) q^{98} +(4.57160 - 7.40918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 704 q - 16 q^{6} - 24 q^{7} + 12 q^{10} + 10 q^{12} + 32 q^{15} - 72 q^{16} + 6 q^{18} + 64 q^{22} - 8 q^{25} + 24 q^{28} + 8 q^{30} - 16 q^{31} + 44 q^{33} - 240 q^{36} + 16 q^{40} - 78 q^{42} - 8 q^{46}+ \cdots - 80 q^{97}+O(q^{100}) $ 704 * q - 16 * q^6 - 24 * q^7 + 12 * q^10 + 10 * q^12 + 32 * q^15 - 72 * q^16 + 6 * q^18 + 64 * q^22 - 8 * q^25 + 24 * q^28 + 8 * q^30 - 16 * q^31 + 44 * q^33 - 240 * q^36 + 16 * q^40 - 78 * q^42 - 8 * q^46 - 20 * q^48 - 60 * q^52 + 272 * q^55 + 8 * q^57 - 20 * q^58 - 14 * q^60 + 12 * q^63 - 84 * q^66 + 112 * q^70 - 38 * q^72 + 104 * q^73 - 64 * q^76 - 16 * q^78 - 168 * q^81 - 72 * q^82 - 64 * q^87 + 52 * q^88 - 44 * q^90 + 40 * q^96 - 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.40478	−	0.163037i	−0.993332	−	0.115285i
$2$	−1.40478	−	0.163037i	−0.993332	−	0.115285i
$3$	0.0253219	−	1.73187i	0.0146196	−	0.999893i
$3$	0.0253219	−	1.73187i	0.0146196	−	0.999893i
$4$	1.94684	+	0.458064i	0.973419	+	0.229032i
$5$	−1.11326	−	1.93924i	−0.497865	−	0.867254i
$5$	−1.11326	−	1.93924i	−0.497865	−	0.867254i
$6$	−0.317930	+	2.42877i	−0.129794	+	0.991541i
$7$	0.130595	+	2.64253i	0.0493603	+	0.998781i
$7$	0.130595	+	2.64253i	0.0493603	+	0.998781i
$8$	−2.66021	−	0.960888i	−0.940525	−	0.339725i
$9$	−2.99872	−	0.0877081i	−0.999573	−	0.0292360i
$10$	1.24772	+	2.90572i	0.394565	+	0.918868i
$11$	−1.45101	+	2.51322i	−0.437496	+	0.757765i	−0.997496	−	0.0707274i	$-0.977468\pi$
$11$	−1.45101	+	2.51322i	−0.437496	+	0.757765i	0.560000	+	0.828493i	$0.310801\pi$
$12$	0.842603	−	3.36006i	0.243238	−	0.969967i
$13$	−1.13395	+	1.13395i	−0.314501	+	0.314501i	−0.846651	−	0.532149i	$-0.821385\pi$
$13$	−1.13395	+	1.13395i	−0.314501	+	0.314501i	0.532149	+	0.846651i	$0.321385\pi$
$14$	0.247372	−	3.73347i	0.0661129	−	0.997812i
$15$	−3.38669	+	1.87891i	−0.874440	+	0.485133i
$16$	3.58035	+	1.78355i	0.895089	+	0.445888i
$17$	5.80269	−	1.55483i	1.40736	−	0.377101i	0.526377	−	0.850251i	$-0.323550\pi$
$17$	5.80269	−	1.55483i	1.40736	−	0.377101i	0.880982	+	0.473150i	$0.156883\pi$
$18$	4.19825	+	0.612113i	0.989537	+	0.144276i
$19$	4.22157	+	7.31197i	0.968495	+	1.67748i	0.699917	+	0.714224i	$0.253220\pi$
$19$	4.22157	+	7.31197i	0.968495	+	1.67748i	0.268577	+	0.963258i	$0.413447\pi$
$20$	−1.27904	−	4.28533i	−0.286002	−	0.958229i
$21$	4.57981	−	0.159259i	0.999396	−	0.0347533i
$22$	2.44811	−	3.29397i	0.521938	−	0.702276i
$23$	−0.212513	−	0.0569428i	−0.0443121	−	0.0118734i	0.236595	−	0.971608i	$-0.423969\pi$
$23$	−0.212513	−	0.0569428i	−0.0443121	−	0.0118734i	−0.280907	+	0.959735i	$0.590635\pi$
$24$	−1.73149	+	4.58279i	−0.353439	+	0.935458i
$25$	−2.52130	+	4.31776i	−0.504260	+	0.863552i
$26$	1.77783	−	1.40808i	0.348662	−	0.276147i
$27$	−0.227832	+	5.19116i	−0.0438462	+	0.999038i
$28$	−0.956199	+	5.20439i	−0.180705	+	0.983537i
$29$			5.64627i			1.04849i	0.851569	+	0.524243i	$0.175652\pi$
$29$			5.64627i			1.04849i	−0.851569	+	0.524243i	$0.824348\pi$
$30$	5.06391	−	2.08731i	0.924538	−	0.381089i
$31$	3.40485	−	5.89737i	0.611529	−	1.05920i	−0.379454	−	0.925211i	$-0.623888\pi$
$31$	3.40485	−	5.89737i	0.611529	−	1.05920i	0.990983	−	0.133988i	$-0.0427785\pi$
$32$	−4.73884	−	3.08924i	−0.837717	−	0.546105i
$33$	4.31582	+	2.57659i	0.751288	+	0.448528i
$34$	−8.40502	+	1.23814i	−1.44145	+	0.212339i
$35$	4.97911	−	3.19508i	0.841622	−	0.540066i
$36$	−5.79784	−	1.54436i	−0.966307	−	0.257393i
$37$	1.79632	−	6.70395i	0.295313	−	1.10212i	−0.645656	−	0.763629i	$-0.723416\pi$
$37$	1.79632	−	6.70395i	0.295313	−	1.10212i	0.940969	−	0.338494i	$-0.109918\pi$
$38$	−4.73827	−	10.9600i	−0.768649	−	1.77795i
$39$	1.93514	+	1.99256i	0.309870	+	0.319066i
$40$	1.09811	+	6.22850i	0.173626	+	0.984812i
$41$			4.91810i			0.768078i	0.923317	+	0.384039i	$0.125467\pi$
$41$			4.91810i			0.768078i	−0.923317	+	0.384039i	$0.874533\pi$
$42$	−6.45961	−	0.522953i	−0.996739	−	0.0806935i
$43$	−0.826434	+	0.826434i	−0.126030	+	0.126030i	−0.767308	−	0.641278i	$-0.778404\pi$
$43$	−0.826434	+	0.826434i	−0.126030	+	0.126030i	0.641278	+	0.767308i	$0.278404\pi$
$44$	−3.97610	+	4.22818i	−0.599420	+	0.637423i
$45$	3.16827	+	5.91287i	0.472297	+	0.881439i
$46$	0.289251	+	0.114640i	0.0426478	+	0.0169027i
$47$	1.31230	−	4.89758i	0.191419	−	0.714386i	−0.801746	−	0.597665i	$-0.796095\pi$
$47$	1.31230	−	4.89758i	0.191419	−	0.714386i	0.993165	−	0.116721i	$-0.0372382\pi$
$48$	3.17953	−	6.15553i	0.458926	−	0.888474i
$49$	−6.96589	+	0.690202i	−0.995127	+	0.0986003i
$50$	4.24584	−	5.65445i	0.600452	−	0.799660i
$51$	−2.54581	−	10.0889i	−0.356485	−	1.41272i
$52$	−2.72704	+	1.68820i	−0.378173	+	0.234111i
$53$	−6.91130	+	1.85188i	−0.949340	+	0.254375i	−0.700082	−	0.714062i	$-0.746853\pi$
$53$	−6.91130	+	1.85188i	−0.949340	+	0.254375i	−0.249258	+	0.968437i	$0.580187\pi$
$54$	1.16641	−	7.25531i	0.158728	−	0.987322i
$55$	6.48910	+	0.0159840i	0.874990	+	0.00215528i
$56$	2.19176	−	7.15515i	0.292886	−	0.956147i
$57$	12.7703	−	7.12604i	1.69146	−	0.943867i
$58$	0.920551	−	7.93179i	0.120874	−	1.04149i
$59$	0.222735	+	0.128596i	0.0289976	+	0.0167418i	0.514429	−	0.857533i	$-0.328004\pi$
$59$	0.222735	+	0.128596i	0.0289976	+	0.0167418i	−0.485431	+	0.874275i	$0.661337\pi$
$60$	−7.45400	+	2.10662i	−0.962308	+	0.271963i
$61$	0.0940230	−	0.0542842i	0.0120384	−	0.00695038i	−0.493969	−	0.869480i	$-0.664454\pi$
$61$	0.0940230	−	0.0542842i	0.0120384	−	0.00695038i	0.506007	+	0.862529i	$0.331121\pi$
$62$	−5.74457	+	7.72942i	−0.729561	+	0.981637i
$63$	−0.159847	−	7.93564i	−0.0201388	−	0.999797i
$64$	6.15339	+	5.11232i	0.769174	+	0.639040i
$65$	3.46139	+	0.936620i	0.429332	+	0.116173i
$66$	−5.64272	−	4.32320i	−0.694571	−	0.532149i
$67$	14.3124	−	3.83501i	1.74854	−	0.468521i	0.764229	−	0.644945i	$-0.223120\pi$
$67$	14.3124	−	3.83501i	1.74854	−	0.468521i	0.984314	+	0.176424i	$0.0564530\pi$
$68$	12.0091	−	0.368991i	1.45632	−	0.0447467i
$69$	−0.103998	+	0.366603i	−0.0125199	+	0.0441338i
$70$	−7.51549	+	3.67661i	−0.898272	+	0.439439i
$71$			12.8900i			1.52976i	0.644174	+	0.764879i	$0.277201\pi$
$71$			12.8900i			1.52976i	−0.644174	+	0.764879i	$0.722799\pi$
$72$	7.89293	+	3.11475i	0.930190	+	0.367077i
$73$	0.272865	−	0.0731140i	0.0319365	−	0.00855735i	−0.242815	−	0.970073i	$-0.578071\pi$
$73$	0.272865	−	0.0731140i	0.0319365	−	0.00855735i	0.274752	+	0.961515i	$0.411404\pi$
$74$	−3.61643	+	9.12474i	−0.420402	+	1.06073i
$75$	7.41393	+	4.47589i	0.856087	+	0.516831i
$76$	4.86936	+	16.1690i	0.558554	+	1.85471i
$77$	−6.83075	−	3.50612i	−0.778437	−	0.399559i
$78$	−2.39359	−	3.11462i	−0.271021	−	0.352662i
$79$	−0.639229	+	0.369059i	−0.0719188	+	0.0415224i	−0.535528	−	0.844517i	$-0.679887\pi$
$79$	−0.639229	+	0.369059i	−0.0719188	+	0.0415224i	0.463609	+	0.886040i	$0.346554\pi$
$80$	−0.527132	−	8.92873i	−0.0589352	−	0.998262i
$81$	8.98461	+	0.526024i	0.998291	+	0.0584471i
$82$	0.801832	−	6.90886i	0.0885476	−	0.762956i
$83$	2.53311	+	2.53311i	0.278044	+	0.278044i	0.832328	−	0.554283i	$-0.187008\pi$
$83$	2.53311	+	2.53311i	0.278044	+	0.278044i	−0.554283	+	0.832328i	$0.687008\pi$
$84$	8.98909	+	1.78779i	0.980790	+	0.195064i
$85$	−9.47509	−	9.52188i	−1.02772	−	1.03279i
$86$	1.29570	−	1.02622i	0.139719	−	0.110660i
$87$	9.77857	+	0.142974i	1.04837	+	0.0153284i
$88$	6.27491	−	5.29143i	0.668908	−	0.564069i
$89$	0.894453	+	1.54924i	0.0948118	+	0.164219i	0.909530	−	0.415638i	$-0.136442\pi$
$89$	0.894453	+	1.54924i	0.0948118	+	0.164219i	−0.814718	+	0.579857i	$0.803108\pi$
$90$	−3.48671	−	8.82286i	−0.367532	−	0.930011i
$91$	−3.14458	−	2.84841i	−0.329642	−	0.298594i
$92$	−0.387645	−	0.208203i	−0.0404148	−	0.0217067i
$93$	−10.1272	−	6.04607i	−1.05015	−	0.626949i
$94$	−2.64199	+	6.66609i	−0.272501	+	0.687555i
$95$	9.47996	−	16.3268i	0.972624	−	1.67509i
$96$	−5.47014	+	8.12881i	−0.558294	+	0.829643i
$97$	−7.84637	+	7.84637i	−0.796678	+	0.796678i	−0.982570	−	0.185892i	$-0.940482\pi$
$97$	−7.84637	+	7.84637i	−0.796678	+	0.796678i	0.185892	+	0.982570i	$0.440482\pi$
$98$	9.89810	+	0.166114i	0.999859	+	0.0167800i
$99$	4.57160	−	7.40918i	0.459463	−	0.744651i
$100$	−6.88637	+	7.25106i	−0.688637	+	0.725106i
$101$	−3.81946	+	6.61550i	−0.380050	+	0.658266i	−0.991069	−	0.133350i	$-0.957427\pi$
$101$	−3.81946	+	6.61550i	−0.380050	+	0.658266i	0.611019	+	0.791616i	$0.290760\pi$
$102$	1.93146	+	14.5877i	0.191243	+	1.44440i
$103$	−1.28360	+	4.79046i	−0.126477	+	0.472018i	−0.999888	−	0.0149657i	$-0.995236\pi$
$103$	−1.28360	+	4.79046i	−0.126477	+	0.472018i	0.873411	+	0.486983i	$0.161903\pi$
$104$	4.10614	−	1.92694i	0.402640	−	0.188952i
$105$	−5.40736	−	8.70405i	−0.527704	−	0.849428i
$106$	10.0108	−	1.47469i	0.972336	−	0.143235i
$107$	11.4675	+	3.07272i	1.10861	+	0.297051i	0.766265	−	0.642524i	$-0.222113\pi$
$107$	11.4675	+	3.07272i	1.10861	+	0.297051i	0.342343	+	0.939575i	$0.388779\pi$
$108$	−2.82143	+	10.0020i	−0.271492	+	0.962441i
$109$	0.363912	−	0.630315i	0.0348565	−	0.0603732i	−0.848071	−	0.529883i	$-0.822236\pi$
$109$	0.363912	−	0.630315i	0.0348565	−	0.0603732i	0.882927	+	0.469510i	$0.155569\pi$
$110$	−9.11317	−	1.08042i	−0.868907	−	0.103014i
$111$	−11.5649	−	3.28074i	−1.09769	−	0.311394i
$112$	−4.24551	+	9.69410i	−0.401163	+	0.916007i
$113$	5.60075	−	5.60075i	0.526874	−	0.526874i	−0.392765	−	0.919639i	$-0.628481\pi$
$113$	5.60075	−	5.60075i	0.526874	−	0.526874i	0.919639	+	0.392765i	$0.128481\pi$
$114$	−19.1013	+	7.92852i	−1.78900	+	0.742574i
$115$	0.126157	+	0.475506i	0.0117642	+	0.0443412i
$116$	−2.58635	+	10.9924i	−0.240137	+	1.02062i
$117$	3.49986	−	3.30094i	0.323562	−	0.305172i
$118$	−0.291928	−	0.216964i	−0.0268742	−	0.0199731i
$119$	4.86647	+	15.1307i	0.446109	+	1.38703i
$120$	10.8147	−	1.74406i	0.987245	−	0.159210i
$121$	1.28914	+	2.23285i	0.117194	+	0.202987i
$122$	−0.140932	+	0.0609284i	−0.0127594	+	0.00551620i
$123$	8.51748	+	0.124535i	0.767996	+	0.0112290i
$124$	9.33006	−	9.92159i	0.837864	−	0.890985i
$125$	11.1800	+	0.0826176i	0.999973	+	0.00738954i
$126$	−1.06925	+	11.1739i	−0.0952567	+	0.995453i
$127$	1.42008	−	1.42008i	0.126012	−	0.126012i	−0.641288	−	0.767300i	$-0.721600\pi$
$127$	1.42008	−	1.42008i	0.126012	−	0.126012i	0.767300	+	0.641288i	$0.221600\pi$
$128$	−7.81069	−	8.18494i	−0.690374	−	0.723453i
$129$	1.41035	+	1.45220i	0.124174	+	0.127859i
$130$	−4.70980	−	1.88008i	−0.413077	−	0.164894i
$131$	7.93273	+	13.7399i	0.693086	+	1.20046i	0.970822	+	0.239803i	$0.0770829\pi$
$131$	7.93273	+	13.7399i	0.693086	+	1.20046i	−0.277735	+	0.960658i	$0.589584\pi$
$132$	7.22196	+	6.99314i	0.628591	+	0.608674i
$133$	−18.7708	+	12.1105i	−1.62763	+	1.05012i
$134$	−20.7311	+	3.05390i	−1.79090	+	0.263817i
$135$	10.3205	−	5.33729i	0.888250	−	0.459361i
$136$	−16.9304	−	1.43958i	−1.45177	−	0.123443i
$137$	12.3083	−	3.29800i	1.05157	−	0.281768i	0.308670	−	0.951169i	$-0.400116\pi$
$137$	12.3083	−	3.29800i	1.05157	−	0.281768i	0.742901	+	0.669402i	$0.233449\pi$
$138$	0.205865	−	0.498042i	0.0175244	−	0.0423961i
$139$	12.8707			1.09168			0.545841	−	0.837889i	$-0.316210\pi$
$139$	12.8707			1.09168			0.545841	+	0.837889i	$0.316210\pi$
$140$	11.1571	−	3.93955i	0.942944	−	0.332952i
$141$	−8.44873	−	2.39675i	−0.711511	−	0.201843i
$142$	2.10154	−	18.1076i	0.176358	−	1.51956i
$143$	−1.20450	−	4.49525i	−0.100725	−	0.375912i
$144$	−10.5800	−	5.66240i	−0.881670	−	0.471866i
$145$	10.9495	−	6.28577i	0.909303	−	0.522004i
$146$	−0.395237	+	0.0582223i	−0.0327101	+	0.00481851i
$147$	1.01895	+	12.0815i	0.0840414	+	0.996462i
$148$	6.56798	−	12.2287i	0.539885	−	1.00519i
$149$	9.13264	−	5.27273i	0.748175	−	0.431959i	−0.0768593	−	0.997042i	$-0.524489\pi$
$149$	9.13264	−	5.27273i	0.748175	−	0.431959i	0.825034	+	0.565083i	$0.191156\pi$
$150$	−9.68524	−	7.49641i	−0.790797	−	0.612079i
$151$	6.51901	−	11.2913i	0.530509	−	0.918869i	−0.468857	−	0.883274i	$-0.655334\pi$
$151$	6.51901	−	11.2913i	0.530509	−	0.918869i	0.999366	−	0.0355952i	$-0.0113327\pi$
$152$	−4.20426	−	23.5078i	−0.341010	−	1.90674i
$153$	−17.5370	+	4.15354i	−1.41778	+	0.335794i
$154$	9.02411	+	6.03901i	0.727183	+	0.486637i
$155$	−15.2269	−	0.0375070i	−1.22305	−	0.00301264i
$156$	2.85468	+	4.76562i	0.228557	+	0.381555i
$157$	−21.8085	+	5.84357i	−1.74051	+	0.466368i	−0.982560	−	0.185946i	$-0.940465\pi$
$157$	−21.8085	+	5.84357i	−1.74051	+	0.466368i	−0.757949	+	0.652314i	$0.773798\pi$
$158$	0.958149	−	0.414230i	0.0762262	−	0.0329544i
$159$	3.03220	+	12.0163i	0.240469	+	0.952957i
$160$	−0.715207	+	12.6289i	−0.0565421	+	0.998400i
$161$	0.122720	−	0.569008i	0.00967165	−	0.0448441i
$162$	−12.5357	−	2.20378i	−0.984896	−	0.173145i
$163$	−12.3322	−	3.30441i	−0.965935	−	0.258821i	−0.258824	−	0.965924i	$-0.583335\pi$
$163$	−12.3322	−	3.30441i	−0.965935	−	0.258821i	−0.707111	+	0.707103i	$0.750002\pi$
$164$	−2.25280	+	9.57474i	−0.175914	+	0.747661i
$165$	0.191998	−	11.2378i	0.0149470	−	0.874865i
$166$	−3.14548	−	3.97146i	−0.244136	−	0.308245i
$167$	2.51803	+	2.51803i	0.194851	+	0.194851i	0.797789	−	0.602937i	$-0.206003\pi$
$167$	2.51803	+	2.51803i	0.194851	+	0.194851i	−0.602937	+	0.797789i	$0.706003\pi$
$168$	−12.3363	−	3.97702i	−0.951763	−	0.306834i
$169$			10.4283i			0.802178i
$170$	11.7580	+	14.9210i	0.901800	+	1.14439i
$171$	−12.0180	−	22.2968i	−0.919038	−	1.70508i
$172$	−1.98749	+	1.23037i	−0.151545	+	0.0938150i
$173$	−4.53432	+	16.9223i	−0.344738	+	1.28658i	0.548181	+	0.836360i	$0.315321\pi$
$173$	−4.53432	+	16.9223i	−0.344738	+	1.28658i	−0.892918	+	0.450219i	$0.851346\pi$
$174$	−13.7135	−	1.79512i	−1.03962	−	0.136088i
$175$	−11.7391	−	6.09873i	−0.887390	−	0.461020i
$176$	−9.67760	+	6.41028i	−0.729476	+	0.483193i
$177$	0.228351	−	0.382490i	0.0171639	−	0.0287497i
$178$	−1.00393	−	2.32217i	−0.0752477	−	0.174054i
$179$	−13.9186	−	8.03591i	−1.04033	−	0.600632i	−0.120400	−	0.992725i	$-0.538418\pi$
$179$	−13.9186	−	8.03591i	−1.04033	−	0.600632i	−0.919925	+	0.392093i	$0.871751\pi$
$180$	3.45963	+	12.9627i	0.257865	+	0.966181i
$181$			5.54727i			0.412326i	0.978518	+	0.206163i	$0.0660977\pi$
$181$			5.54727i			0.412326i	−0.978518	+	0.206163i	$0.933902\pi$
$182$	3.95307	+	4.51408i	0.293021	+	0.334606i
$183$	−0.0916321	−	0.164210i	−0.00677364	−	0.0121387i
$184$	0.510613	+	0.355681i	0.0376429	+	0.0262211i
$185$	−15.0003	+	3.97975i	−1.10285	+	0.292597i
$186$	13.2408	+	10.1445i	0.970866	+	0.743834i
$187$	−4.51214	+	16.8395i	−0.329960	+	1.23143i
$188$	4.79825	−	8.93368i	0.349948	−	0.651556i
$189$	−13.7475	+	0.0758879i	−0.999985	+	0.00552003i
$190$	−15.9792	+	21.3900i	−1.15925	+	1.55179i
$191$	−0.871209	+	0.502993i	−0.0630385	+	0.0363953i	−0.531188	−	0.847254i	$-0.678254\pi$
$191$	−0.871209	+	0.502993i	−0.0630385	+	0.0363953i	0.468149	+	0.883649i	$0.344921\pi$
$192$	9.00967	−	10.5274i	0.650217	−	0.759749i
$193$	−2.85804	+	0.765809i	−0.205726	+	0.0551241i	−0.360210	−	0.932871i	$-0.617295\pi$
$193$	−2.85804	+	0.765809i	−0.205726	+	0.0551241i	0.154484	+	0.987995i	$0.450628\pi$
$194$	12.3017	−	9.74320i	0.883211	−	0.699521i
$195$	1.70975	−	5.97094i	0.122438	−	0.427588i
$196$	−13.8776	−	1.84711i	−0.991258	−	0.131937i
$197$	0.223825	−	0.223825i	0.0159469	−	0.0159469i	−0.699088	−	0.715035i	$-0.746411\pi$
$197$	0.223825	−	0.223825i	0.0159469	−	0.0159469i	0.715035	+	0.699088i	$0.246411\pi$
$198$	−7.63008	+	9.66296i	−0.542246	+	0.686717i
$199$	−6.53808	−	3.77477i	−0.463473	−	0.267586i	0.250031	−	0.968238i	$-0.419559\pi$
$199$	−6.53808	−	3.77477i	−0.463473	−	0.267586i	−0.713503	+	0.700652i	$0.752893\pi$
$200$	10.8561	−	9.06344i	0.767640	−	0.640882i
$201$	−6.27930	−	24.8843i	−0.442908	−	1.75521i
$202$	6.44409	−	8.67063i	0.453404	−	0.610063i
$203$	−14.9204	+	0.737374i	−1.04721	+	0.0517535i
$204$	−0.334950	−	20.8075i	−0.0234512	−	1.45682i
$205$	9.53737	−	5.47512i	0.666119	−	0.382399i
$206$	2.58420	−	6.52028i	0.180050	−	0.454290i
$207$	0.632273	+	0.189394i	0.0439460	+	0.0131638i
$208$	−6.08241	+	2.03749i	−0.421739	+	0.141274i
$209$	−24.5022			−1.69485
$210$	6.17709	+	13.1089i	0.426260	+	0.904601i
$211$			9.81539i			0.675719i	0.941197	+	0.337860i	$0.109703\pi$
$211$			9.81539i			0.675719i	−0.941197	+	0.337860i	$0.890297\pi$
$212$	−14.3035	+	0.439487i	−0.982365	+	0.0301841i
$213$	22.3237	+	0.326398i	1.52959	+	0.0223644i
$214$	−15.6084	−	6.18614i	−1.06697	−	0.422876i
$215$	2.52269	+	0.682617i	0.172046	+	0.0465541i
$216$	5.59420	−	13.5906i	0.380637	−	0.924725i
$217$	16.0286	+	8.22723i	1.08809	+	0.558501i
$218$	−0.613983	+	0.826125i	−0.0415842	+	0.0559522i
$219$	−0.119714	−	0.474417i	−0.00808954	−	0.0320582i
$220$	12.6259	+	3.00354i	0.851238	+	0.202499i
$221$	−4.81687	+	8.34306i	−0.324018	+	0.561215i
$222$	15.7112	+	6.49423i	1.05447	+	0.435864i
$223$	9.70554	+	9.70554i	0.649931	+	0.649931i	0.952976	−	0.303045i	$-0.0980033\pi$
$223$	9.70554	+	9.70554i	0.649931	+	0.649931i	−0.303045	+	0.952976i	$0.598003\pi$
$224$	7.54452	−	12.9260i	0.504090	−	0.863651i
$225$	7.93937	−	12.7266i	0.529292	−	0.848440i
$226$	−8.78097	+	6.95471i	−0.584101	+	0.462621i
$227$	6.05134	+	22.5839i	0.401642	+	1.49895i	0.810167	+	0.586200i	$0.199377\pi$
$227$	6.05134	+	22.5839i	0.401642	+	1.49895i	−0.408525	+	0.912747i	$0.633957\pi$
$228$	28.1258	−	8.02365i	1.86268	−	0.531379i
$229$	−12.2351	−	21.1919i	−0.808521	−	1.40040i	−0.913888	−	0.405965i	$-0.866935\pi$
$229$	−12.2351	−	21.1919i	−0.808521	−	1.40040i	0.105368	−	0.994433i	$-0.466398\pi$
$230$	−0.0996982	−	0.688552i	−0.00657390	−	0.0454018i
$231$	−6.24509	+	11.7412i	−0.410897	+	0.772512i
$232$	5.42543	−	15.0202i	0.356197	−	0.986126i
$233$	−27.4604	−	7.35799i	−1.79899	−	0.482038i	−0.805169	−	0.593045i	$-0.797926\pi$
$233$	−27.4604	−	7.35799i	−1.79899	−	0.482038i	−0.993820	+	0.111007i	$0.964592\pi$
$234$	−5.45472	+	4.06651i	−0.356586	+	0.265836i
$235$	−10.9585	+	2.90742i	−0.714855	+	0.189659i
$236$	0.374723	+	0.352382i	0.0243924	+	0.0229381i
$237$	0.622974	+	1.11640i	0.0404665	+	0.0725182i
$238$	−4.36948	−	22.0488i	−0.283231	−	1.42921i
$239$	−21.9771			−1.42158			−0.710790	−	0.703404i	$-0.751662\pi$
$239$	−21.9771			−1.42158			−0.710790	+	0.703404i	$0.751662\pi$
$240$	−15.4767	+	0.686830i	−0.999017	+	0.0443347i
$241$	9.91219	−	17.1684i	0.638500	−	1.10591i	−0.347262	−	0.937768i	$-0.612888\pi$
$241$	9.91219	−	17.1684i	0.638500	−	1.10591i	0.985762	−	0.168147i	$-0.0537782\pi$
$242$	−1.44692	−	3.34685i	−0.0930117	−	0.215144i
$243$	1.13851	−	15.5468i	0.0730354	−	0.997329i
$244$	0.207913	−	0.0626140i	0.0133103	−	0.00400845i
$245$	9.09332	+	12.7402i	0.580951	+	0.813939i
$246$	−11.9449	−	1.56361i	−0.761580	−	0.0996922i
$247$	−13.0785	−	3.50437i	−0.832164	−	0.222978i
$248$	−14.7243	+	12.4165i	−0.934995	+	0.788451i
$249$	4.45114	−	4.32286i	0.282080	−	0.273950i
$250$	−15.6921	−	1.93882i	−0.992453	−	0.122622i
$251$	12.6489			0.798389			0.399194	−	0.916866i	$-0.369290\pi$
$251$	12.6489			0.798389			0.399194	+	0.916866i	$0.369290\pi$
$252$	3.32384	−	15.5226i	0.209382	−	0.977834i
$253$	0.451469	−	0.451469i	0.0283836	−	0.0283836i
$254$	−2.22643	+	1.76338i	−0.139699	+	0.110644i
$255$	−16.7305	+	16.1685i	−1.04771	+	1.01251i
$256$	9.63788	+	12.7715i	0.602368	+	0.798219i
$257$	−4.48386	+	16.7340i	−0.279696	+	1.04384i	0.672933	+	0.739703i	$0.265034\pi$
$257$	−4.48386	+	16.7340i	−0.279696	+	1.04384i	−0.952629	+	0.304135i	$0.901633\pi$
$258$	−1.74447	−	2.26996i	−0.108606	−	0.141322i
$259$	17.9500	+	3.87132i	1.11536	+	0.240552i
$260$	6.30973	+	3.40898i	0.391313	+	0.211416i
$261$	0.495223	−	16.9316i	0.0306536	−	1.04804i
$262$	−8.90367	−	20.5949i	−0.550070	−	1.27236i
$263$	0.909279	+	3.39348i	0.0560685	+	0.209251i	0.988277	−	0.152671i	$-0.0487875\pi$
$263$	0.909279	+	3.39348i	0.0560685	+	0.209251i	−0.932209	+	0.361922i	$0.882121\pi$
$264$	−9.00516	−	11.0013i	−0.554229	−	0.677083i
$265$	11.2853	+	11.3410i	0.693251	+	0.696675i
$266$	28.3433	−	13.9523i	1.73784	−	0.855472i
$267$	2.70572	−	1.50984i	0.165587	−	0.0924009i
$268$	29.6207	−	0.910123i	1.80937	−	0.0555946i
$269$	−10.3821	−	5.99413i	−0.633010	−	0.365468i	0.148907	−	0.988851i	$-0.452425\pi$
$269$	−10.3821	−	5.99413i	−0.633010	−	0.365468i	−0.781917	+	0.623383i	$0.785758\pi$
$270$	−15.3683	+	5.81511i	−0.935285	+	0.353896i
$271$	14.4142	+	24.9662i	0.875603	+	1.51659i	0.856119	+	0.516778i	$0.172869\pi$
$271$	14.4142	+	24.9662i	0.875603	+	1.51659i	0.0194834	+	0.999810i	$0.493798\pi$
$272$	23.5488	+	4.78257i	1.42786	+	0.289986i
$273$	−5.01269	+	5.37387i	−0.303382	+	0.325241i
$274$	−17.8282	+	2.62627i	−1.07704	+	0.158659i
$275$	−7.19306	−	12.6017i	−0.433758	−	0.759912i
$276$	−0.370395	+	0.666078i	−0.0222952	+	0.0400932i
$277$	5.13004	−	1.37459i	0.308234	−	0.0825912i	−0.101386	−	0.994847i	$-0.532328\pi$
$277$	5.13004	−	1.37459i	0.308234	−	0.0825912i	0.409621	+	0.912256i	$0.365661\pi$
$278$	−18.0806	−	2.09841i	−1.08440	−	0.125854i
$279$	−10.7274	+	17.3859i	−0.642234	+	1.04087i
$280$	−16.3156	+	3.71520i	−0.975041	+	0.222025i
$281$		−	7.77124i		−	0.463593i	−0.972764	−	0.231797i	$-0.925540\pi$
$281$		−	7.77124i		−	0.463593i	0.972764	−	0.231797i	$-0.0744604\pi$
$282$	11.4779	+	4.74437i	0.683498	+	0.282523i
$283$	−1.86661	−	6.96629i	−0.110959	−	0.414103i	0.887994	−	0.459854i	$-0.152098\pi$
$283$	−1.86661	−	6.96629i	−0.110959	−	0.414103i	−0.998953	+	0.0457515i	$0.985432\pi$
$284$	−5.90443	+	25.0947i	−0.350363	+	1.48909i
$285$	−28.0357	−	16.8314i	−1.66069	−	0.997009i
$286$	0.959168	+	6.51123i	0.0567168	+	0.385017i
$287$	−12.9962	+	0.642279i	−0.767141	+	0.0379125i
$288$	13.9395	+	9.67939i	0.821393	+	0.570363i
$289$	16.5313	−	9.54435i	0.972429	−	0.561432i
$290$	−16.4064	+	7.04498i	−0.963420	+	0.413695i
$291$	13.3902	+	13.7875i	0.784946	+	0.808240i
$292$	0.564715	−	0.0173514i	0.0330475	−	0.00101541i
$293$	−2.16784	−	2.16784i	−0.126647	−	0.126647i	0.640942	−	0.767589i	$-0.278544\pi$
$293$	−2.16784	−	2.16784i	−0.126647	−	0.126647i	−0.767589	+	0.640942i	$0.778544\pi$
$294$	0.538325	−	17.1380i	0.0313958	−	0.999507i
$295$	0.00141658	−	0.575097i	8.24767e−5	−	0.0334834i
$296$	−11.2203	+	16.1078i	−0.652168	+	0.936249i
$297$	−12.7159	−	8.10501i	−0.737854	−	0.470301i
$298$	−13.6890	+	5.91809i	−0.792985	+	0.342826i
$299$	0.305550	−	0.176409i	0.0176704	−	0.0102020i
$300$	12.3835	+	12.1099i	0.714961	+	0.699165i
$301$	−2.29180	−	2.07594i	−0.132097	−	0.119655i
$302$	−10.9987	+	14.7989i	−0.632904	+	0.851583i
$303$	11.3604	+	6.78231i	0.652640	+	0.389633i
$304$	2.07343	+	33.7089i	0.118919	+	1.93334i
$305$	−0.209942	−	0.121901i	−0.0120213	−	0.00698001i
$306$	25.3129	−	2.97565i	1.44704	−	0.170106i
$307$	13.4650	+	13.4650i	0.768488	+	0.768488i	0.977840	−	0.209352i	$-0.0671356\pi$
$307$	13.4650	+	13.4650i	0.768488	+	0.768488i	−0.209352	+	0.977840i	$0.567136\pi$
$308$	−11.6923	−	9.95477i	−0.666233	−	0.567225i
$309$	8.26392	+	2.34432i	0.470118	+	0.133364i
$310$	21.3844	+	2.53524i	1.21455	+	0.143992i
$311$	−21.4184	−	12.3659i	−1.21453	−	0.701207i	−0.250784	−	0.968043i	$-0.580688\pi$
$311$	−21.4184	−	12.3659i	−1.21453	−	0.701207i	−0.963742	+	0.266836i	$0.914022\pi$
$312$	−3.23323	−	7.16008i	−0.183046	−	0.405360i
$313$	1.49481	−	5.57869i	0.0844914	−	0.315326i	−0.910726	−	0.413011i	$-0.864477\pi$
$313$	1.49481	−	5.57869i	0.0844914	−	0.315326i	0.995217	+	0.0976849i	$0.0311437\pi$
$314$	31.5890	−	4.65336i	1.78267	−	0.262604i
$315$	−15.2112	+	9.14442i	−0.857052	+	0.515230i
$316$	−1.41353	+	0.425690i	−0.0795171	+	0.0239469i
$317$	−8.11509	−	2.17443i	−0.455789	−	0.122128i	0.0236178	−	0.999721i	$-0.492482\pi$
$317$	−8.11509	−	2.17443i	−0.455789	−	0.122128i	−0.479407	+	0.877593i	$0.659148\pi$
$318$	−2.30047	−	17.3747i	−0.129004	−	0.974326i
$319$	−14.1903	−	8.19279i	−0.794506	−	0.458708i
$320$	3.06369	−	17.6242i	0.171265	−	0.985225i
$321$	5.61191	−	19.7824i	0.313226	−	1.10415i
$322$	−0.265164	+	0.779326i	−0.0147770	+	0.0434301i
$323$	35.8653	+	35.8653i	1.99560	+	1.99560i
$324$	17.2506	+	5.13961i	0.958369	+	0.285534i
$325$	−2.03709	−	7.75516i	−0.112998	−	0.430179i
$326$	16.7854	+	6.65259i	0.929656	+	0.368453i
$327$	−1.08241	−	0.646208i	−0.0598571	−	0.0357354i
$328$	4.72574	−	13.0831i	0.260935	−	0.722396i
$329$	13.1134	+	2.82820i	0.722964	+	0.155923i
$330$	−2.10190	+	15.7554i	−0.115706	+	0.867308i
$331$	17.0561	−	9.84732i	0.937486	−	0.541258i	0.0483146	−	0.998832i	$-0.484615\pi$
$331$	17.0561	−	9.84732i	0.937486	−	0.541258i	0.889171	+	0.457574i	$0.151282\pi$
$332$	3.77122	+	6.09187i	0.206973	+	0.334335i
$333$	−5.97464	+	19.9457i	−0.327408	+	1.09302i
$334$	−3.12676	−	3.94783i	−0.171089	−	0.216016i
$335$	−23.3705	−	23.4859i	−1.27687	−	1.28317i
$336$	16.6814	+	7.59812i	0.910044	+	0.414512i
$337$	−16.5999	+	16.5999i	−0.904254	+	0.904254i	−0.995801	−	0.0915467i	$-0.970819\pi$
$337$	−16.5999	+	16.5999i	−0.904254	+	0.904254i	0.0915467	+	0.995801i	$0.470819\pi$
$338$	1.70020	−	14.6495i	0.0924788	−	0.796829i
$339$	−9.55792	−	9.84156i	−0.519115	−	0.534520i
$340$	−14.0848	−	22.8778i	−0.763857	−	1.24072i
$341$	9.88094	+	17.1143i	0.535083	+	0.926791i
$342$	13.2475	+	33.2816i	0.716341	+	1.79966i
$343$	−2.73359	−	18.3174i	−0.147600	−	0.989047i
$344$	2.99259	−	1.40437i	0.161350	−	0.0757187i
$345$	0.826707	−	0.206446i	0.0445084	−	0.0111147i
$346$	9.12870	−	23.0329i	0.490762	−	1.23826i
$347$	−2.69541	−	10.0594i	−0.144697	−	0.540017i	−0.999769	−	0.0215069i	$-0.993154\pi$
$347$	−2.69541	−	10.0594i	−0.144697	−	0.540017i	0.855072	−	0.518510i	$-0.173513\pi$
$348$	18.9718	+	4.75756i	1.01700	+	0.255032i
$349$	10.8818			0.582490			0.291245	−	0.956648i	$-0.405931\pi$
$349$	10.8818			0.582490			0.291245	+	0.956648i	$0.405931\pi$
$350$	15.4965	+	10.4813i	0.828324	+	0.560249i
$351$	−5.62817	−	6.14487i	−0.300409	−	0.327989i
$352$	14.6401	−	7.42725i	0.780317	−	0.395874i
$353$	−3.61853	−	13.5045i	−0.192595	−	0.718774i	−0.992876	−	0.119149i	$-0.961983\pi$
$353$	−3.61853	−	13.5045i	−0.192595	−	0.718774i	0.800282	−	0.599624i	$-0.204683\pi$
$354$	−0.383144	+	0.500087i	−0.0203639	+	0.0265793i
$355$	24.9967	−	14.3499i	1.32669	−	0.761613i
$356$	1.03170	+	3.42583i	0.0546802	+	0.181569i
$357$	26.3276	−	8.04494i	1.39340	−	0.425783i
$358$	18.2425	+	13.5580i	0.964145	+	0.716561i
$359$	11.2996	+	19.5714i	0.596369	+	1.03294i	0.993352	+	0.115115i	$0.0367238\pi$
$359$	11.2996	+	19.5714i	0.596369	+	1.03294i	−0.396983	+	0.917826i	$0.629943\pi$
$360$	−2.74663	−	18.7738i	−0.144760	−	0.989467i
$361$	−26.1433	+	45.2815i	−1.37596	+	2.38324i
$362$	0.904412	−	7.79272i	0.0475348	−	0.409576i
$363$	3.89964	−	2.17607i	0.204678	−	0.114214i
$364$	−4.81724	−	6.98581i	−0.252492	−	0.366156i
$365$	−0.445556	−	0.447756i	−0.0233215	−	0.0234366i
$366$	0.101951	+	0.245619i	0.00532907	+	0.0128387i
$367$	−0.931738	−	3.47729i	−0.0486363	−	0.181513i	0.937335	−	0.348431i	$-0.113285\pi$
$367$	−0.931738	−	3.47729i	−0.0486363	−	0.181513i	−0.985971	+	0.166917i	$0.946619\pi$
$368$	−0.659312	−	0.582904i	−0.0343690	−	0.0303860i
$369$	0.431357	−	14.7480i	0.0224555	−	0.767749i
$370$	21.7211	−	3.14508i	1.12923	−	0.163505i
$371$	−5.79622	−	18.0214i	−0.300925	−	0.935627i
$372$	−16.9466	−	16.4096i	−0.878640	−	0.850801i
$373$	7.02234	+	1.88163i	0.363603	+	0.0974272i	0.435995	−	0.899949i	$-0.356397\pi$
$373$	7.02234	+	1.88163i	0.363603	+	0.0974272i	−0.0723918	+	0.997376i	$0.523063\pi$
$374$	9.08405	−	22.9203i	0.469725	−	1.18518i
$375$	0.426182	−	19.3602i	0.0220079	−	0.999758i
$376$	−8.19703	+	11.7676i	−0.422729	+	0.606868i
$377$	−6.40259	−	6.40259i	−0.329750	−	0.329750i
$378$	19.3247	+	2.13475i	0.993954	+	0.109800i
$379$	−11.0602			−0.568127			−0.284063	−	0.958805i	$-0.591683\pi$
$379$	−11.0602			−0.568127			−0.284063	+	0.958805i	$0.591683\pi$
$380$	25.9347	−	27.4431i	1.33042	−	1.40780i
$381$	−2.42343	−	2.49535i	−0.124156	−	0.127841i
$382$	1.30587	−	0.564557i	0.0668140	−	0.0288853i
$383$	27.3567	+	7.33022i	1.39786	+	0.374557i	0.877577	−	0.479435i	$-0.159158\pi$
$383$	27.3567	+	7.33022i	1.39786	+	0.374557i	0.520287	+	0.853992i	$0.325825\pi$
$384$	−14.3730	+	13.3198i	−0.733469	+	0.679723i
$385$	0.805206	+	17.1497i	0.0410371	+	0.874029i
$386$	4.13978	−	0.609830i	0.210709	−	0.0310395i
$387$	2.55073	−	2.40576i	0.129661	−	0.122291i
$388$	−18.8697	+	11.6815i	−0.957966	+	0.593037i
$389$	26.9026	+	15.5322i	1.36402	+	0.787516i	0.990156	−	0.139969i	$-0.0447004\pi$
$389$	26.9026	+	15.5322i	1.36402	+	0.787516i	0.373861	+	0.927485i	$0.378034\pi$
$390$	−3.37531	+	8.10913i	−0.170916	+	0.410622i
$391$	−1.32168			−0.0668405
$392$	19.1939	+	4.85736i	0.969439	+	0.245334i
$393$	23.9965	−	13.3905i	1.21046	−	0.675462i
$394$	−0.350918	+	0.277935i	−0.0176790	+	0.0140021i
$395$	1.42732	+	0.828759i	0.0718163	+	0.0416994i
$396$	12.2940	−	12.3304i	0.617799	−	0.619626i
$397$	−3.82532	+	14.2763i	−0.191987	+	0.716507i	0.801039	+	0.598612i	$0.204281\pi$
$397$	−3.82532	+	14.2763i	−0.191987	+	0.716507i	−0.993026	+	0.117894i	$0.962386\pi$
$398$	8.56917	+	6.36868i	0.429534	+	0.319233i
$399$	20.4985	+	32.8151i	1.02621	+	1.64281i
$400$	−16.7281	+	10.9622i	−0.836405	+	0.548112i
$401$	27.1101	−	15.6520i	1.35381	−	0.781625i	0.365032	−	0.930995i	$-0.381058\pi$
$401$	27.1101	−	15.6520i	1.35381	−	0.781625i	0.988781	+	0.149370i	$0.0477246\pi$
$402$	4.76399	+	35.9809i	0.237606	+	1.79456i
$403$	2.82640	+	10.5483i	0.140793	+	0.525446i
$404$	−10.4662	+	11.1297i	−0.520712	+	0.553725i
$405$	−8.98213	−	18.0089i	−0.446326	−	0.894871i
$406$	21.0802	+	1.39673i	1.04619	+	0.0693184i
$407$	14.2421	+	14.2421i	0.705952	+	0.705952i
$408$	−2.92186	+	29.2847i	−0.144654	+	1.44981i
$409$	−9.50820	−	5.48956i	−0.470150	−	0.271441i	0.246152	−	0.969231i	$-0.420834\pi$
$409$	−9.50820	−	5.48956i	−0.470150	−	0.271441i	−0.716303	+	0.697790i	$0.754167\pi$
$410$	−14.2906	+	6.13642i	−0.705762	+	0.303056i
$411$	−5.40003	−	21.3999i	−0.266364	−	1.05558i
$412$	−4.69329	+	8.73827i	−0.231222	+	0.430504i
$413$	−0.310730	+	0.605376i	−0.0152900	+	0.0297886i
$414$	−0.857329	−	0.369142i	−0.0421354	−	0.0181423i
$415$	2.09229	−	7.73231i	0.102707	−	0.379564i
$416$	8.87666	−	1.87057i	0.435214	−	0.0917122i
$417$	0.325911	−	22.2904i	0.0159599	−	1.09157i
$418$	34.4203	+	3.99476i	1.68355	+	0.195390i
$419$		−	19.5632i		−	0.955725i	−0.878435	−	0.477862i	$-0.841412\pi$
$419$		−	19.5632i		−	0.955725i	0.878435	−	0.477862i	$-0.158588\pi$
$420$	−6.54025	−	19.4223i	−0.319131	−	0.947711i
$421$		−	22.3584i		−	1.08968i	−0.838540	−	0.544841i	$-0.816590\pi$
$421$		−	22.3584i		−	1.08968i	0.838540	−	0.544841i	$-0.183410\pi$
$422$	1.60027	−	13.7885i	0.0779000	−	0.671214i
$423$	−4.36479	+	14.5714i	−0.212223	+	0.708484i
$424$	20.1649	+	1.71461i	0.979295	+	0.0832688i
$425$	−7.91697	+	28.9748i	−0.384029	+	1.40548i
$426$	−31.3068	−	4.09811i	−1.51682	−	0.198554i
$427$	0.155726	+	0.241369i	0.00753613	+	0.0116807i
$428$	20.9179	+	11.2349i	1.01111	+	0.543062i
$429$	−7.81567	+	1.97220i	−0.377344	+	0.0952188i
$430$	−3.43254	−	1.37022i	−0.165532	−	0.0660779i
$431$	−15.3247	−	8.84771i	−0.738164	−	0.426179i	0.0832375	−	0.996530i	$-0.473474\pi$
$431$	−15.3247	−	8.84771i	−0.738164	−	0.426179i	−0.821401	+	0.570351i	$0.806807\pi$
$432$	−10.0744	+	18.1798i	−0.484706	+	0.874677i
$433$	−12.3670	−	12.3670i	−0.594321	−	0.594321i	0.344475	−	0.938796i	$-0.388057\pi$
$433$	−12.3670	−	12.3670i	−0.594321	−	0.594321i	−0.938796	+	0.344475i	$0.888057\pi$
$434$	−21.1754	−	14.1707i	−1.01645	−	0.680218i
$435$	−10.6088	−	19.1222i	−0.508655	−	0.916838i
$436$	0.997203	−	1.06043i	0.0477573	−	0.0507852i
$437$	−0.480776	−	1.79428i	−0.0229986	−	0.0858320i
$438$	0.0908250	+	0.685972i	0.00433979	+	0.0327770i
$439$	23.8365	−	13.7620i	1.13765	−	0.656824i	0.191804	−	0.981433i	$-0.438566\pi$
$439$	23.8365	−	13.7620i	1.13765	−	0.656824i	0.945848	+	0.324610i	$0.105233\pi$
$440$	−17.2470	−	6.27781i	−0.822217	−	0.299283i
$441$	20.9493	−	1.45876i	0.997584	−	0.0694645i
$442$	8.12689	−	10.9349i	0.386557	−	0.520119i
$443$	−1.71669	+	6.40676i	−0.0815623	+	0.304395i	−0.994641	−	0.103389i	$-0.967031\pi$
$443$	−1.71669	+	6.40676i	−0.0815623	+	0.304395i	0.913079	+	0.407783i	$0.133698\pi$
$444$	−21.0121	−	11.6845i	−0.997191	−	0.554522i
$445$	2.00858	−	3.45926i	0.0952160	−	0.163985i
$446$	−12.0518	−	15.2166i	−0.570671	−	0.720525i
$447$	−8.90041	−	15.9500i	−0.420975	−	0.754410i
$448$	−12.7058	+	16.9281i	−0.600294	+	0.799779i
$449$	7.52323			0.355043			0.177522	−	0.984117i	$-0.443192\pi$
$449$	7.52323			0.355043			0.177522	+	0.984117i	$0.443192\pi$
$450$	−13.2280	+	16.5837i	−0.623575	+	0.781764i
$451$	−12.3603	−	7.13621i	−0.582023	−	0.336031i
$452$	13.4692	−	8.33825i	0.633540	−	0.392198i
$453$	−19.3899	−	11.5760i	−0.911015	−	0.543886i
$454$	−4.81881	−	32.7121i	−0.226158	−	1.53526i
$455$	−2.02300	+	9.26912i	−0.0948398	+	0.434543i
$456$	−40.8188	+	6.68595i	−1.91152	+	0.313098i
$457$	−12.5227	−	3.35544i	−0.585787	−	0.156961i	−0.0462598	−	0.998929i	$-0.514730\pi$
$457$	−12.5227	−	3.35544i	−0.585787	−	0.156961i	−0.539527	+	0.841968i	$0.681397\pi$
$458$	13.7327	+	31.7648i	0.641685	+	1.48427i
$459$	6.74931	+	30.4769i	0.315031	+	1.42254i
$460$	0.0277949	+	0.983522i	0.00129594	+	0.0458569i
$461$	2.20357			0.102631			0.0513154	−	0.998682i	$-0.483659\pi$
$461$	2.20357			0.102631			0.0513154	+	0.998682i	$0.483659\pi$
$462$	10.6873	−	15.4756i	0.497216	−	0.719991i
$463$	−18.5485	−	18.5485i	−0.862022	−	0.862022i	0.129551	−	0.991573i	$-0.458646\pi$
$463$	−18.5485	−	18.5485i	−0.862022	−	0.862022i	−0.991573	+	0.129551i	$0.958646\pi$
$464$	−10.0704	+	20.2156i	−0.467507	+	0.938487i
$465$	−0.450530	+	26.3700i	−0.0208929	+	1.22288i
$466$	37.3763	+	14.8134i	1.73142	+	0.686219i
$467$	−15.6941	−	4.20523i	−0.726237	−	0.194595i	−0.123284	−	0.992371i	$-0.539343\pi$
$467$	−15.6941	−	4.20523i	−0.726237	−	0.194595i	−0.602953	+	0.797777i	$0.706009\pi$
$468$	8.32569	−	4.82324i	0.384855	−	0.222954i
$469$	12.0032	+	37.3202i	0.554258	+	1.72329i
$470$	15.8684	−	2.29765i	0.731954	−	0.105982i
$471$	9.56805	+	37.9174i	0.440873	+	1.74714i
$472$	−0.468954	−	0.556115i	−0.0215853	−	0.0255973i
$473$	−0.877849	−	3.27618i	−0.0403635	−	0.150639i
$474$	−0.693129	−	1.66987i	−0.0318365	−	0.0766999i
$475$	−42.2152	−	0.207971i	−1.93697	−	0.00954236i
$476$	2.54340	+	31.6862i	0.116576	+	1.45233i
$477$	20.8875	−	4.94708i	0.956371	−	0.226511i
$478$	30.8731	+	3.58308i	1.41210	+	0.163886i
$479$	3.64119	−	6.30672i	0.166370	−	0.288162i	−0.770771	−	0.637112i	$-0.780129\pi$
$479$	3.64119	−	6.30672i	0.166370	−	0.288162i	0.937141	+	0.348951i	$0.113462\pi$
$480$	21.8534	+	1.55843i	0.997467	+	0.0711322i
$481$	5.56502	+	9.63889i	0.253743	+	0.439496i
$482$	−16.7236	+	22.5019i	−0.761738	+	1.02493i
$483$	−0.982338	−	0.226942i	−0.0446979	−	0.0103262i
$484$	1.48695	+	4.93751i	0.0675888	+	0.224432i
$485$	23.9510	+	6.48094i	1.08756	+	0.294284i
$486$	−4.13407	+	21.6543i	−0.187525	+	0.982260i
$487$	0.250033	+	0.933137i	0.0113301	+	0.0422845i	0.971359	−	0.237615i	$-0.0763656\pi$
$487$	0.250033	+	0.933137i	0.0113301	+	0.0422845i	−0.960029	+	0.279899i	$0.909699\pi$
$488$	−0.302282	+	0.0540616i	−0.0136836	+	0.00244725i
$489$	−6.03507	+	21.2741i	−0.272915	+	0.962048i
$490$	−10.6970	−	19.3797i	−0.483243	−	0.875486i
$491$	−25.5058			−1.15106			−0.575530	−	0.817780i	$-0.695204\pi$
$491$	−25.5058			−1.15106			−0.575530	+	0.817780i	$0.695204\pi$
$492$	16.5251	+	4.14400i	0.745010	+	0.186826i
$493$	8.77896	+	32.7635i	0.395385	+	1.47560i
$494$	17.8011	+	7.05516i	0.800909	+	0.317427i
$495$	−19.4576	−	0.617078i	−0.874553	−	0.0277356i
$496$	22.7088	−	15.0420i	1.01966	−	0.675404i
$497$	−34.0621	+	1.68337i	−1.52789	+	0.0755093i
$498$	−6.95768	+	5.34698i	−0.311781	+	0.239604i
$499$	−8.06052	−	13.9612i	−0.360838	−	0.624991i	0.627261	−	0.778809i	$-0.284176\pi$
$499$	−8.06052	−	13.9612i	−0.360838	−	0.624991i	−0.988099	+	0.153819i	$0.950843\pi$
$500$	21.7279	+	5.28201i	0.971700	+	0.236219i
$501$	4.42466	−	4.29714i	0.197679	−	0.191982i
$502$	−17.7689	−	2.06223i	−0.793065	−	0.0920420i
$503$	−17.3143	+	17.3143i	−0.772009	+	0.772009i	−0.978457	−	0.206449i	$-0.933809\pi$
$503$	−17.3143	+	17.3143i	−0.772009	+	0.772009i	0.206449	+	0.978457i	$0.433809\pi$
$504$	−7.20004	+	21.2640i	−0.320715	+	0.947176i
$505$	17.0811	+	0.0420743i	0.760098	+	0.00187228i
$506$	−0.707822	+	0.560610i	−0.0314665	+	0.0249222i
$507$	18.0604	+	0.264064i	0.802092	+	0.0117275i
$508$	3.41515	−	2.11418i	0.151523	−	0.0938015i
$509$	1.06802	−	0.616621i	0.0473391	−	0.0273312i	−0.476144	−	0.879368i	$-0.657966\pi$
$509$	1.06802	−	0.616621i	0.0473391	−	0.0273312i	0.523483	+	0.852036i	$0.324632\pi$
$510$	26.1389	−	19.9855i	1.15745	−	0.884973i
$511$	0.228841	+	0.711505i	0.0101233	+	0.0314751i
$512$	−11.4569	−	19.5125i	−0.506329	−	0.862340i
$513$	−38.9194	+	20.2489i	−1.71833	+	0.894012i
$514$	9.02712	−	22.7766i	0.398169	−	1.00463i
$515$	10.7188	−	2.84382i	0.472328	−	0.125314i
$516$	2.08051	+	3.47322i	0.0915895	+	0.152900i
$517$	10.4046	+	10.4046i	0.457592	+	0.457592i
$518$	−24.5847	−	8.36487i	−1.08019	−	0.367531i
$519$	29.1923	+	8.28133i	1.28140	+	0.363510i
$520$	−8.30801	−	5.81761i	−0.364330	−	0.255119i
$521$	19.0507	+	10.9989i	0.834624	+	0.481871i	0.855433	−	0.517913i	$-0.173291\pi$
$521$	19.0507	+	10.9989i	0.834624	+	0.481871i	−0.0208090	+	0.999783i	$0.506624\pi$
$522$	−3.45615	+	23.7044i	−0.151272	+	1.03752i
$523$	17.7524	+	4.75673i	0.776257	+	0.207997i	0.625134	−	0.780518i	$-0.285044\pi$
$523$	17.7524	+	4.75673i	0.776257	+	0.207997i	0.151123	+	0.988515i	$0.451711\pi$
$524$	9.15000	+	30.3831i	0.399719	+	1.32729i
$525$	−10.8594	+	20.1760i	−0.473944	+	0.880555i
$526$	−0.724078	−	4.91535i	−0.0315713	−	0.214319i
$527$	10.5879	−	39.5146i	0.461216	−	1.72128i
$528$	10.8567	+	16.9226i	0.472477	+	0.736463i
$529$	−19.8767	−	11.4758i	−0.864203	−	0.498948i
$530$	−14.0044	−	17.7716i	−0.608313	−	0.771951i
$531$	−0.656640	−	0.405159i	−0.0284957	−	0.0175824i
$532$	−42.0910	+	14.9790i	−1.82488	+	0.649422i
$533$	−5.57688	−	5.57688i	−0.241562	−	0.241562i
$534$	−4.04712	+	1.67987i	−0.175136	+	0.0726951i
$535$	−6.80762	−	25.6590i	−0.294319	−	1.10934i
$536$	−41.7591	−	3.55074i	−1.80372	−	0.153369i
$537$	−14.2696	+	23.9017i	−0.615777	+	1.03143i
$538$	13.6074	+	10.1131i	0.586656	+	0.436008i
$539$	8.37295	−	18.5083i	0.360648	−	0.797210i
$540$	22.5372	−	5.66337i	0.969847	−	0.243713i
$541$	11.3081	−	6.52873i	0.486173	−	0.280692i	−0.236812	−	0.971555i	$-0.576103\pi$
$541$	11.3081	−	6.52873i	0.486173	−	0.280692i	0.722985	+	0.690863i	$0.242769\pi$
$542$	−16.1785	−	37.4222i	−0.694925	−	1.60742i
$543$	9.60713	+	0.140467i	0.412282	+	0.00602803i
$544$	−32.3012	−	10.5578i	−1.38490	−	0.452662i
$545$	−1.62746	−	0.00400877i	−0.0697127	−	0.000171717i
$546$	7.91788	−	6.73187i	0.338854	−	0.288098i
$547$	−20.7705	−	20.7705i	−0.888084	−	0.888084i	0.106255	−	0.994339i	$-0.466114\pi$
$547$	−20.7705	−	20.7705i	−0.888084	−	0.888084i	−0.994339	+	0.106255i	$0.966114\pi$
$548$	25.4730	−	0.782682i	1.08815	−	0.0334345i
$549$	−0.286710	+	0.154536i	−0.0122365	+	0.00659546i
$550$	8.05015	+	18.8754i	0.343260	+	0.804850i
$551$	−41.2854	+	23.8361i	−1.75882	+	1.01545i
$552$	0.628921	−	0.875307i	0.0267687	−	0.0372555i
$553$	−1.05873	−	1.64098i	−0.0450217	−	0.0697816i
$554$	−7.43071	+	1.09462i	−0.315701	+	0.0465058i
$555$	6.51256	+	26.0793i	0.276443	+	1.10701i
$556$	25.0572	+	5.89562i	1.06266	+	0.250030i
$557$	−10.4281	−	38.9181i	−0.441852	−	1.64901i	−0.724117	−	0.689678i	$-0.757752\pi$
$557$	−10.4281	−	38.9181i	−0.441852	−	1.64901i	0.282265	−	0.959337i	$-0.408914\pi$
$558$	17.9043	−	22.6745i	0.757948	−	0.959888i
$559$		−	1.87427i		−	0.0792732i
$560$	23.5255	−	2.55901i	0.994136	−	0.108138i
$561$	29.0495	+	8.24082i	1.22647	+	0.347928i
$562$	−1.26700	+	10.9169i	−0.0534452	+	0.460502i
$563$	−27.0643	+	7.25186i	−1.14062	+	0.305629i	−0.779202	−	0.626773i	$-0.784375\pi$
$563$	−27.0643	+	7.25186i	−1.14062	+	0.305629i	−0.361422	+	0.932402i	$0.617709\pi$
$564$	−15.3504	−	8.53614i	−0.646370	−	0.359436i
$565$	−17.0963	−	4.62610i	−0.719246	−	0.194621i
$566$	1.48642	+	10.0905i	0.0624790	+	0.424134i
$567$	−0.216685	+	23.8108i	−0.00909991	+	0.999959i
$568$	12.3858	−	34.2900i	0.519697	−	1.43877i
$569$	−7.97346	−	13.8104i	−0.334265	−	0.578963i	0.649079	−	0.760721i	$-0.275155\pi$
$569$	−7.97346	−	13.8104i	−0.334265	−	0.578963i	−0.983343	+	0.181758i	$0.941821\pi$
$570$	36.6400	+	28.2154i	1.53468	+	1.18181i
$571$	−11.8613	−	6.84810i	−0.496378	−	0.286584i	0.230838	−	0.972992i	$-0.425853\pi$
$571$	−11.8613	−	6.84810i	−0.496378	−	0.286584i	−0.727217	+	0.686408i	$0.759186\pi$
$572$	−0.285851	−	9.30326i	−0.0119520	−	0.388989i
$573$	0.849056	+	1.52155i	0.0354698	+	0.0635638i
$574$	18.3616	+	1.21660i	0.766397	+	0.0507799i
$575$	0.781675	−	0.774011i	0.0325981	−	0.0322785i
$576$	−18.0039	−	15.8701i	−0.750162	−	0.661254i
$577$	7.53859	+	28.1344i	0.313836	+	1.17125i	0.925069	+	0.379800i	$0.124007\pi$
$577$	7.53859	+	28.1344i	0.313836	+	1.17125i	−0.611233	+	0.791450i	$0.709326\pi$
$578$	−24.7790	+	10.7125i	−1.03067	+	0.445583i
$579$	1.25391	+	4.96913i	0.0521106	+	0.206510i
$580$	24.1961	−	7.22181i	1.00469	−	0.299869i
$581$	−6.36299	+	7.02461i	−0.263981	+	0.291430i
$582$	−16.5624	−	21.5516i	−0.686534	−	0.893343i
$583$	5.37419	−	20.0567i	0.222576	−	0.830665i
$584$	−0.796132	−	0.0676946i	−0.0329442	−	0.00280122i
$585$	−10.2976	−	3.11225i	−0.425752	−	0.128676i
$586$	2.69191	+	3.39879i	0.111202	+	0.140403i
$587$	21.1699	−	21.1699i	0.873774	−	0.873774i	−0.119108	−	0.992881i	$-0.538003\pi$
$587$	21.1699	−	21.1699i	0.873774	−	0.873774i	0.992881	+	0.119108i	$0.0380034\pi$
$588$	−3.55036	+	23.9874i	−0.146414	+	0.989223i
$589$	57.4952			2.36905
$590$	−0.0957521	+	0.807656i	−0.00394205	+	0.0332507i
$591$	−0.381968	−	0.393303i	−0.0157121	−	0.0161783i
$592$	18.3883	−	20.7987i	0.755755	−	0.854821i
$593$	−9.42723	−	2.52602i	−0.387130	−	0.103731i	0.0600040	−	0.998198i	$-0.480889\pi$
$593$	−9.42723	−	2.52602i	−0.387130	−	0.103731i	−0.447134	+	0.894467i	$0.647555\pi$
$594$	16.5417	+	13.4590i	0.678716	+	0.552228i
$595$	23.9244	−	26.2817i	0.980806	−	1.07744i
$596$	20.1950	−	6.08182i	0.827220	−	0.249121i
$597$	−6.70294	+	11.2275i	−0.274333	+	0.459511i
$598$	−0.457993	+	0.198001i	−0.0187287	+	0.00809687i
$599$	12.1948	−	21.1219i	0.498264	−	0.863019i	−0.501734	−	0.865022i	$-0.667304\pi$
$599$	12.1948	−	21.1219i	0.498264	−	0.863019i	0.999998	+	0.00200297i	$0.000637565\pi$
$600$	−15.4218	−	19.0307i	−0.629591	−	0.776927i
$601$	−27.4637			−1.12027			−0.560133	−	0.828402i	$-0.689250\pi$
$601$	−27.4637			−1.12027			−0.560133	+	0.828402i	$0.689250\pi$
$602$	2.88103	+	3.28990i	0.117422	+	0.134086i
$603$	−43.2553	+	10.2448i	−1.76149	+	0.417200i
$604$	17.8636	−	18.9961i	0.726858	−	0.772941i
$605$	2.89489	−	4.98569i	0.117694	−	0.202697i
$606$	−14.8532	−	11.3798i	−0.603370	−	0.462275i
$607$	−15.4174	−	4.13108i	−0.625772	−	0.167675i	−0.0680219	−	0.997684i	$-0.521669\pi$
$607$	−15.4174	−	4.13108i	−0.625772	−	0.167675i	−0.557751	+	0.830009i	$0.688335\pi$
$608$	2.58307	−	47.6917i	0.104757	−	1.93415i
$609$	0.899221	+	25.8588i	0.0364383	+	1.04785i
$610$	0.275049	+	0.205473i	0.0111364	+	0.00831934i
$611$	4.06553	+	7.04171i	0.164474	+	0.284877i
$612$	−36.0443	+	0.0532037i	−1.45700	+	0.00215063i
$613$	−9.47562	−	35.3635i	−0.382717	−	1.42832i	−0.841735	−	0.539891i	$-0.818465\pi$
$613$	−9.47562	−	35.3635i	−0.382717	−	1.42832i	0.459018	−	0.888427i	$-0.348201\pi$
$614$	−16.7201	−	21.1107i	−0.674769	−	0.851959i
$615$	−9.24067	−	16.6561i	−0.372620	−	0.671638i
$616$	14.8022	+	15.8906i	0.596399	+	0.640250i
$617$	−15.9157	−	15.9157i	−0.640742	−	0.640742i	0.309996	−	0.950738i	$-0.399672\pi$
$617$	−15.9157	−	15.9157i	−0.640742	−	0.640742i	−0.950738	+	0.309996i	$0.899672\pi$
$618$	−11.2268	−	4.64060i	−0.451609	−	0.186672i
$619$	18.3083	−	31.7110i	0.735875	−	1.27457i	−0.218464	−	0.975845i	$-0.570105\pi$
$619$	18.3083	−	31.7110i	0.735875	−	1.27457i	0.954339	−	0.298727i	$-0.0965621\pi$
$620$	−29.6271	−	7.04791i	−1.18985	−	0.283051i
$621$	0.344016	−	1.09022i	0.0138049	−	0.0437489i
$622$	28.0721	+	20.8634i	1.12559	+	0.836548i
$623$	−3.97709	+	2.56594i	−0.159339	+	0.102802i
$624$	3.37463	+	10.5855i	0.135093	+	0.423759i
$625$	−12.2861	−	21.7727i	−0.491443	−	0.870910i
$626$	−3.00941	+	7.59315i	−0.120280	+	0.303483i
$627$	−0.620440	+	42.4345i	−0.0247780	+	1.69467i
$628$	−45.1344	+	1.38680i	−1.80106	+	0.0553392i
$629$		−	41.6939i		−	1.66245i
$630$	22.8593	−	10.3660i	0.910736	−	0.412990i
$631$	11.7112			0.466216			0.233108	−	0.972451i	$-0.425110\pi$
$631$	11.7112			0.466216			0.233108	+	0.972451i	$0.425110\pi$
$632$	2.05510	−	0.367545i	0.0817476	−	0.0146202i
$633$	16.9989	+	0.248544i	0.675647	+	0.00987873i
$634$	11.0454	+	4.37767i	0.438671	+	0.173860i
$635$	−4.33480	−	1.17296i	−0.172021	−	0.0465474i
$636$	0.398942	+	24.7828i	0.0158191	+	0.982702i
$637$	7.11632	−	8.68163i	0.281959	−	0.343979i
$638$	18.5986	+	13.8227i	0.736327	+	0.547244i
$639$	1.13055	−	38.6534i	0.0447240	−	1.52910i
$640$	−7.17722	+	24.2588i	−0.283705	+	0.958912i
$641$	13.4136	+	7.74433i	0.529804	+	0.305882i	0.740937	−	0.671575i	$-0.234382\pi$
$641$	13.4136	+	7.74433i	0.529804	+	0.305882i	−0.211133	+	0.977457i	$0.567715\pi$
$642$	−11.1088	+	26.8751i	−0.438429	+	1.06068i
$643$	−22.0638	+	22.0638i	−0.870110	+	0.870110i	−0.992484	−	0.122374i	$-0.960949\pi$
$643$	−22.0638	+	22.0638i	−0.870110	+	0.870110i	0.122374	+	0.992484i	$0.460949\pi$
$644$	0.499557	−	1.05155i	0.0196853	−	0.0414370i
$645$	1.24608	−	4.35167i	0.0490643	−	0.171347i
$646$	−44.5356	−	56.2304i	−1.75223	−	2.21236i
$647$	43.9896	−	11.7870i	1.72941	−	0.463394i	0.749364	−	0.662159i	$-0.230359\pi$
$647$	43.9896	−	11.7870i	1.72941	−	0.463394i	0.980047	+	0.198764i	$0.0636928\pi$
$648$	−23.3955	−	10.0325i	−0.919061	−	0.394115i
$649$	−0.646381	+	0.373188i	−0.0253727	+	0.0146489i
$650$	1.59730	+	11.2264i	0.0626512	+	0.440338i
$651$	14.6543	−	27.5511i	0.574349	−	1.07981i
$652$	−22.4952	−	12.0821i	−0.880981	−	0.473172i
$653$	4.96517	−	18.5303i	0.194302	−	0.725145i	−0.798144	−	0.602466i	$-0.794185\pi$
$653$	4.96517	−	18.5303i	0.194302	−	0.725145i	0.992446	−	0.122679i	$-0.0391486\pi$
$654$	1.41519	+	1.08426i	0.0553383	+	0.0423977i
$655$	17.8138	−	30.6796i	0.696041	−	1.19875i
$656$	−8.77168	+	17.6085i	−0.342477	+	0.687498i
$657$	−0.824659	+	0.195316i	−0.0321730	+	0.00762000i
$658$	−17.9604	−	6.11097i	−0.700168	−	0.238230i
$659$			13.1520i			0.512329i	0.966633	+	0.256164i	$0.0824588\pi$
$659$			13.1520i			0.512329i	−0.966633	+	0.256164i	$0.917541\pi$
$660$	5.52144	−	21.7903i	0.214922	−	0.848186i
$661$	33.7694	+	19.4967i	1.31348	+	0.758336i	0.982670	−	0.185363i	$-0.0593462\pi$
$661$	33.7694	+	19.4967i	1.31348	+	0.758336i	0.330806	+	0.943699i	$0.392680\pi$
$662$	−25.5656	+	11.0526i	−0.993634	+	0.429571i
$663$	14.3271	+	8.55343i	0.556418	+	0.332188i
$664$	−4.30455	−	9.17261i	−0.167049	−	0.355966i
$665$	44.3820	+	22.9189i	1.72106	+	0.888755i
$666$	11.6450	−	27.0453i	0.451234	−	1.04799i
$667$	0.321514	−	1.19991i	0.0124491	−	0.0464606i
$668$	3.74878	+	6.05562i	0.145045	+	0.234299i
$669$	17.0545	−	16.5629i	0.659363	−	0.640360i
$670$	29.0014	+	36.8029i	1.12042	+	1.42182i
$671$			0.315068i			0.0121631i
$672$	−22.1950	−	13.3934i	−0.856190	−	0.516662i
$673$	4.22536	+	4.22536i	0.162876	+	0.162876i	0.783839	−	0.620964i	$-0.213259\pi$
$673$	4.22536	+	4.22536i	0.162876	+	0.162876i	−0.620964	+	0.783839i	$0.713259\pi$
$674$	26.0257	−	20.6129i	1.00247	−	0.793978i
$675$	−21.8397	−	14.0722i	−0.840611	−	0.541639i
$676$	−4.77683	+	20.3022i	−0.183724	+	0.780855i
$677$	1.85651	+	0.497451i	0.0713516	+	0.0191186i	0.294318	−	0.955707i	$-0.404907\pi$
$677$	1.85651	+	0.497451i	0.0713516	+	0.0191186i	−0.222967	+	0.974826i	$0.571574\pi$
$678$	11.8223	+	15.3836i	0.454032	+	0.590802i
$679$	−21.7589	−	19.7095i	−0.835031	−	0.756382i
$680$	16.0562	+	34.4347i	0.615728	+	1.32051i
$681$	39.2655	−	9.90824i	1.50466	−	0.379685i
$682$	−11.0903	−	25.6529i	−0.424671	−	0.982298i
$683$	33.1137	−	8.87278i	1.26706	−	0.339507i	0.438156	−	0.898899i	$-0.355632\pi$
$683$	33.1137	−	8.87278i	1.26706	−	0.339507i	0.828903	+	0.559392i	$0.188965\pi$
$684$	−13.1837	−	48.9133i	−0.504091	−	1.87025i
$685$	−20.0980	−	20.1972i	−0.767905	−	0.771697i
$686$	0.853683	+	26.1777i	0.0325938	+	0.999469i
$687$	−37.0113	+	20.6530i	−1.41207	+	0.787961i
$688$	−4.43291	+	1.48494i	−0.169003	+	0.0566127i
$689$	5.73714	−	9.93701i	0.218568	−	0.378570i
$690$	−1.19500	+	0.155228i	−0.0454930	+	0.00590945i
$691$	4.52782	−	2.61414i	0.172246	−	0.0994465i	−0.411398	−	0.911456i	$-0.634959\pi$
$691$	4.52782	−	2.61414i	0.172246	−	0.0994465i	0.583645	+	0.812009i	$0.301626\pi$
$692$	−16.5791	+	30.8680i	−0.630242	+	1.17342i
$693$	20.1760	+	11.1130i	0.766422	+	0.422147i
$694$	2.14641	+	14.5707i	0.0814766	+	0.553098i
$695$	−14.3285	−	24.9595i	−0.543511	−	0.946766i
$696$	−25.8756	−	9.77645i	−0.980813	−	0.370576i
$697$	7.64678	+	28.5382i	0.289643	+	1.08096i
$698$	−15.2866	−	1.77414i	−0.578606	−	0.0671522i
$699$	−13.4384	+	47.3714i	−0.508287	+	1.79175i
$700$	−20.0604	−	17.2505i	−0.758213	−	0.652007i
$701$	−1.34671			−0.0508646			−0.0254323	−	0.999677i	$-0.508096\pi$
$701$	−1.34671			−0.0508646			−0.0254323	+	0.999677i	$0.508096\pi$
$702$	6.90452	+	9.54981i	0.260594	+	0.360434i
$703$	56.6024	−	15.1666i	2.13480	−	0.572018i
$704$	−21.7770	+	8.04681i	−0.820753	+	0.303276i
$705$	4.75776	+	19.0523i	0.179188	+	0.717552i
$706$	2.88151	+	19.5609i	0.108447	+	0.736185i
$707$	−17.9804	−	9.22907i	−0.676223	−	0.347095i
$708$	0.619767	−	0.640047i	0.0232923	−	0.0240544i
$709$	8.53604	+	14.7848i	0.320578	+	0.555257i	0.980607	−	0.195983i	$-0.0627897\pi$
$709$	8.53604	+	14.7848i	0.320578	+	0.555257i	−0.660030	+	0.751239i	$0.729456\pi$
$710$	−37.4546	+	16.0831i	−1.40565	+	0.603588i
$711$	1.94924	−	1.05064i	0.0731021	−	0.0394020i
$712$	−0.890785	−	4.98076i	−0.0333836	−	0.186662i
$713$	−1.05939	+	1.05939i	−0.0396744	+	0.0396744i
$714$	−38.2962	+	7.00903i	−1.43320	+	0.262306i
$715$	−7.37644	+	7.34019i	−0.275863	+	0.274508i
$716$	−23.4163	−	22.0202i	−0.875108	−	0.822934i
$717$	−0.556501	+	38.0614i	−0.0207829	+	1.42143i
$718$	−12.6826	−	29.3359i	−0.473310	−	1.09481i
$719$	7.89970	+	13.6827i	0.294609	+	0.510278i	0.974894	−	0.222670i	$-0.0714773\pi$
$719$	7.89970	+	13.6827i	0.294609	+	0.510278i	−0.680285	+	0.732948i	$0.738144\pi$
$720$	0.797599	+	26.8210i	0.0297247	+	0.999558i
$721$	−12.8265	−	2.76633i	−0.477685	−	0.103024i
$722$	44.1083	−	59.3485i	1.64154	−	2.20872i
$723$	−29.4824	−	17.6013i	−1.09646	−	0.654600i
$724$	−2.54101	+	10.7996i	−0.0944358	+	0.401366i
$725$	−24.3792	−	14.2359i	−0.905421	−	0.528709i
$726$	−5.83294	+	2.42113i	−0.216481	+	0.0898564i
$727$	17.9996	−	17.9996i	0.667568	−	0.667568i	−0.289584	−	0.957153i	$-0.593517\pi$
$727$	17.9996	−	17.9996i	0.667568	−	0.667568i	0.957153	+	0.289584i	$0.0935170\pi$
$728$	5.62824	+	10.5989i	0.208596	+	0.392823i
$729$	−26.8962	−	2.36542i	−0.996155	−	0.0876081i
$730$	0.552909	+	0.701643i	0.0204641	+	0.0259690i
$731$	−3.51058	+	6.08050i	−0.129843	+	0.224895i
$732$	−0.103174	−	0.361663i	−0.00381343	−	0.0133675i
$733$	−27.5147	−	7.37254i	−1.01628	−	0.272311i	−0.288028	−	0.957622i	$-0.593000\pi$
$733$	−27.5147	−	7.37254i	−1.01628	−	0.272311i	−0.728250	+	0.685311i	$0.759666\pi$
$734$	0.741963	+	5.03675i	0.0273863	+	0.185910i
$735$	22.2945	−	15.4258i	0.822345	−	0.568989i
$736$	0.831157	+	0.926346i	0.0306368	+	0.0341456i
$737$	−11.1293	+	41.5350i	−0.409952	+	1.52996i
$738$	−3.01043	+	20.6474i	−0.110816	+	0.760042i
$739$	−22.7657	+	39.4313i	−0.837448	+	1.45050i	0.0545728	+	0.998510i	$0.482620\pi$
$739$	−22.7657	+	39.4313i	−0.837448	+	1.45050i	−0.892021	+	0.451994i	$0.850713\pi$
$740$	−31.0262	+	0.876819i	−1.14055	+	0.0322325i
$741$	−6.40026	+	22.5614i	−0.235120	+	0.828815i
$742$	5.20427	+	26.2612i	0.191055	+	0.964080i
$743$	24.5375	−	24.5375i	0.900195	−	0.900195i	−0.0952576	−	0.995453i	$-0.530367\pi$
$743$	24.5375	−	24.5375i	0.900195	−	0.900195i	0.995453	+	0.0952576i	$0.0303675\pi$
$744$	21.1309	+	25.8149i	0.774698	+	0.946422i
$745$	−20.3921	−	11.8404i	−0.747108	−	0.433800i
$746$	−9.55810	−	3.78819i	−0.349947	−	0.138695i
$747$	−7.37389	−	7.81824i	−0.269797	−	0.286055i
$748$	−16.4980	+	30.7170i	−0.603226	+	1.12312i
$749$	−6.62213	+	30.7045i	−0.241967	+	1.12192i
$750$	−3.75513	+	27.1275i	−0.137118	+	0.990555i
$751$	−2.15854	−	3.73871i	−0.0787663	−	0.136427i	0.823952	−	0.566660i	$-0.191765\pi$
$751$	−2.15854	−	3.73871i	−0.0787663	−	0.136427i	−0.902718	+	0.430233i	$0.858431\pi$
$752$	13.4336	−	15.1945i	0.489873	−	0.554087i
$753$	0.320292	−	21.9061i	0.0116721	−	0.798303i
$754$	7.95040	+	10.0381i	0.289536	+	0.365567i
$755$	−29.1538	−	0.0718119i	−1.06102	−	0.00261350i
$756$	−26.7989	−	6.14950i	−0.974668	−	0.223655i
$757$	13.4640	+	13.4640i	0.489357	+	0.489357i	0.908103	−	0.418746i	$-0.137530\pi$
$757$	13.4640	+	13.4640i	0.489357	+	0.489357i	−0.418746	+	0.908103i	$0.637530\pi$
$758$	15.5373	+	1.80323i	0.564339	+	0.0654963i
$759$	−0.770451	−	0.793315i	−0.0279656	−	0.0287955i
$760$	−40.9068	+	34.3234i	−1.48385	+	1.24504i
$761$	15.6293	−	9.02358i	0.566562	−	0.327104i	−0.189213	−	0.981936i	$-0.560594\pi$
$761$	15.6293	−	9.02358i	0.566562	−	0.327104i	0.755775	+	0.654832i	$0.227260\pi$
$762$	2.99756	+	3.90053i	0.108590	+	0.141301i
$763$	1.71315	+	0.879332i	0.0620201	+	0.0318339i
$764$	−1.92651	+	0.580176i	−0.0696985	+	0.0209900i
$765$	27.5780	+	29.3845i	0.997083	+	1.06240i
$766$	−37.2352	−	14.7575i	−1.34536	−	0.533211i
$767$	−0.398392	+	0.106749i	−0.0143851	+	0.00385447i
$768$	22.3626	−	16.3681i	0.806940	−	0.590634i
$769$			8.60151i			0.310178i	0.987900	+	0.155089i	$0.0495665\pi$
$769$			8.60151i			0.310178i	−0.987900	+	0.155089i	$0.950434\pi$
$770$	1.66490	−	24.2229i	0.0599987	−	0.872933i
$771$	28.8675	+	8.18918i	1.03964	+	0.294926i
$772$	−5.91492	+	0.181742i	−0.212883	+	0.00654102i
$773$	−45.9349	+	12.3082i	−1.65216	+	0.442696i	−0.960218	−	0.279253i	$-0.909913\pi$
$773$	−45.9349	+	12.3082i	−1.65216	+	0.442696i	−0.691946	+	0.721949i	$0.743247\pi$
$774$	−3.97545	+	2.96371i	−0.142894	+	0.106528i
$775$	16.8788	+	29.5704i	0.606303	+	1.06220i
$776$	28.4124	−	13.3335i	1.01995	−	0.478644i
$777$	7.15912	−	30.9889i	0.256832	−	1.11172i
$778$	−35.2600	−	26.2056i	−1.26413	−	0.939515i
$779$	−35.9610	+	20.7621i	−1.28844	+	0.743879i
$780$	6.06368	−	10.8413i	0.217114	−	0.388180i
$781$	−32.3954	−	18.7035i	−1.15920	−	0.669263i
$782$	1.85668	+	0.215484i	0.0663948	+	0.00770568i
$783$	−29.3106	−	1.28640i	−1.04748	−	0.0459721i
$784$	−26.1714	−	9.95286i	−0.934692	−	0.355459i
$785$	35.6106	+	35.7865i	1.27100	+	1.27728i
$786$	−35.8931	+	14.8985i	−1.28026	+	0.531410i
$787$	−20.8181	+	5.57819i	−0.742085	+	0.198841i	−0.610005	−	0.792398i	$-0.708832\pi$
$787$	−20.8181	+	5.57819i	−0.742085	+	0.198841i	−0.132080	+	0.991239i	$0.542166\pi$
$788$	0.538278	−	0.333225i	0.0191754	−	0.0118707i
$789$	5.90007	−	1.48882i	0.210048	−	0.0530034i
$790$	−1.86996	−	1.39693i	−0.0665302	−	0.0497007i
$791$	15.5316	+	14.0687i	0.552238	+	0.500225i
$792$	−19.2808	+	15.3172i	−0.685113	+	0.544271i
$793$	−0.0450619	+	0.168173i	−0.00160019	+	0.00597200i
$794$	7.70132	−	19.4314i	0.273309	−	0.689596i
$795$	19.9269	−	19.2575i	0.706735	−	0.682992i
$796$	−10.9995	−	10.3437i	−0.389867	−	0.366623i
$797$	−22.0767	+	22.0767i	−0.781998	+	0.781998i	−0.980168	−	0.198170i	$-0.936500\pi$
$797$	−22.0767	+	22.0767i	−0.781998	+	0.781998i	0.198170	+	0.980168i	$0.436500\pi$
$798$	−23.4459	−	49.4402i	−0.829975	−	1.75016i
$799$		−	30.4596i		−	1.07758i
$800$	25.2866	−	12.6723i	0.894017	−	0.448032i
$801$	−2.54633	−	4.72418i	−0.0899702	−	0.166921i
$802$	−40.6357	+	17.5678i	−1.43490	+	0.620339i
$803$	−0.212178	+	0.791861i	−0.00748762	+	0.0279442i
$804$	−0.826160	−	51.3221i	−0.0291364	−	1.80999i
$805$	−1.24006	+	0.395472i	−0.0437065	+	0.0139386i
$806$	−2.25072	−	15.2788i	−0.0792783	−	0.538174i
$807$	−10.6439	+	17.8287i	−0.374684	+	0.627599i
$808$	16.5173	−	13.9285i	0.581076	−	0.490003i
$809$	24.8511	−	43.0433i	0.873717	−	1.51332i	0.0155928	−	0.999878i	$-0.495036\pi$
$809$	24.8511	−	43.0433i	0.873717	−	1.51332i	0.858124	−	0.513443i	$-0.171630\pi$
$810$	9.68183	+	26.7631i	0.340185	+	0.940359i
$811$			13.7116i			0.481480i	0.970590	+	0.240740i	$0.0773901\pi$
$811$			13.7116i			0.481480i	−0.970590	+	0.240740i	$0.922610\pi$
$812$	−29.3854	−	5.39895i	−1.03122	−	0.189466i
$813$	43.6031	−	24.3313i	1.52923	−	0.853337i
$814$	−17.6850	−	22.3290i	−0.619860	−	0.782631i
$815$	7.32094	+	27.5938i	0.256441	+	0.966569i
$816$	8.87907	−	40.6623i	0.310830	−	1.42346i
$817$	−9.53171	−	2.55401i	−0.333472	−	0.0893536i
$818$	12.4620	+	9.26184i	0.435723	+	0.323833i
$819$	9.17989	+	8.81737i	0.320771	+	0.308104i
$820$	21.0757	−	6.29045i	0.735994	−	0.219672i
$821$	6.64204	+	11.5044i	0.231809	+	0.401505i	0.958341	−	0.285628i	$-0.0922022\pi$
$821$	6.64204	+	11.5044i	0.231809	+	0.401505i	−0.726532	+	0.687133i	$0.758869\pi$
$822$	4.09691	+	30.9426i	0.142896	+	1.07925i
$823$	−14.7840	+	3.96137i	−0.515339	+	0.138085i	−0.507110	−	0.861882i	$-0.669286\pi$
$823$	−14.7840	+	3.96137i	−0.515339	+	0.138085i	−0.00822895	+	0.999966i	$0.502619\pi$
$824$	8.01773	−	11.5102i	0.279311	−	0.400977i
$825$	−22.0066	+	12.1383i	−0.766172	+	0.422602i
$826$	0.535208	−	0.799763i	0.0186223	−	0.0278273i
$827$	−4.71860	+	4.71860i	−0.164082	+	0.164082i	−0.784372	−	0.620290i	$-0.787015\pi$
$827$	−4.71860	+	4.71860i	−0.164082	+	0.164082i	0.620290	+	0.784372i	$0.287015\pi$
$828$	1.14418	+	0.658342i	0.0397629	+	0.0228789i
$829$	5.22604	−	9.05177i	0.181508	−	0.314381i	−0.760886	−	0.648885i	$-0.775236\pi$
$829$	5.22604	−	9.05177i	0.181508	−	0.314381i	0.942394	+	0.334504i	$0.108569\pi$
$830$	−4.19987	+	10.5211i	−0.145780	+	0.365193i
$831$	−2.25070	−	8.91935i	−0.0780761	−	0.309409i
$832$	−12.7748	+	1.18052i	−0.442885	+	0.0409272i
$833$	−39.3478	+	14.8358i	−1.36332	+	0.514029i
$834$	−4.09200	+	31.2601i	−0.141694	+	1.08245i
$835$	2.07984	−	7.68630i	0.0719759	−	0.265995i
$836$	−47.7018	−	11.2236i	−1.64980	−	0.388175i
$837$	29.8384	+	19.0187i	1.03137	+	0.657383i
$838$	−3.18953	+	27.4821i	−0.110180	+	0.949352i
$839$	27.3107			0.942869			0.471434	−	0.881901i	$-0.343736\pi$
$839$	27.3107			0.942869			0.471434	+	0.881901i	$0.343736\pi$
$840$	6.02108	+	28.3504i	0.207747	+	0.978183i
$841$	−2.88032			−0.0993213
$842$	−3.64525	+	31.4087i	−0.125624	+	1.08242i
$843$	−13.4587	−	0.196782i	−0.463544	−	0.00677754i
$844$	−4.49608	+	19.1090i	−0.154761	+	0.657758i
$845$	20.2230	−	11.6094i	0.695692	−	0.399376i
$846$	8.50726	−	19.7580i	0.292485	−	0.679294i
$847$	−5.73201	+	3.69818i	−0.196954	+	0.127071i
$848$	−28.0478	−	5.69629i	−0.963166	−	0.195611i
$849$	−12.1119	+	3.05632i	−0.415681	+	0.104893i
$850$	15.8456	−	39.4126i	0.543500	−	1.35184i
$851$	−0.763483	+	1.32239i	−0.0261719	+	0.0453310i
$852$	43.3111	+	10.8611i	1.48381	+	0.372096i
$853$	24.3619	−	24.3619i	0.834137	−	0.834137i	−0.153943	−	0.988080i	$-0.549197\pi$
$853$	24.3619	−	24.3619i	0.834137	−	0.834137i	0.988080	+	0.153943i	$0.0491972\pi$
$854$	−0.179410	−	0.364461i	−0.00613928	−	0.0124716i
$855$	−29.8597	+	48.1279i	−1.02118	+	1.64594i
$856$	−27.5535	−	19.1931i	−0.941758	−	0.656006i
$857$	17.8903	−	4.79370i	0.611122	−	0.163750i	0.0600332	−	0.998196i	$-0.480879\pi$
$857$	17.8903	−	4.79370i	0.611122	−	0.163750i	0.551088	+	0.834447i	$0.314213\pi$
$858$	11.3009	−	1.49627i	0.385805	−	0.0510819i
$859$	3.22346	+	5.58319i	0.109983	+	0.190496i	0.915763	−	0.401719i	$-0.131587\pi$
$859$	3.22346	+	5.58319i	0.109983	+	0.190496i	−0.805780	+	0.592215i	$0.798254\pi$
$860$	4.59858	+	2.48450i	0.156810	+	0.0847206i
$861$	0.783253	+	22.5239i	0.0266932	+	0.767614i
$862$	20.0854	+	14.9276i	0.684110	+	0.508437i
$863$	−2.87045	−	0.769134i	−0.0977111	−	0.0261816i	0.209632	−	0.977780i	$-0.432773\pi$
$863$	−2.87045	−	0.769134i	−0.0977111	−	0.0261816i	−0.307343	+	0.951599i	$0.599440\pi$
$864$	17.1164	−	23.8962i	0.582311	−	0.812966i
$865$	37.8643	−	10.0458i	1.28742	−	0.341568i
$866$	15.3567	+	19.3893i	0.521842	+	0.658874i
$867$	−16.1109	−	28.8717i	−0.547156	−	0.980533i
$868$	27.4365	+	23.3592i	0.931256	+	0.792864i
$869$		−	2.14203i		−	0.0726635i
$870$	11.7855	+	28.5922i	0.399566	+	0.969365i
$871$	−11.8809	+	20.5783i	−0.402569	+	0.697270i
$872$	−1.57374	+	1.32709i	−0.0532937	+	0.0449409i
$873$	24.2172	−	22.8408i	0.819629	−	0.773046i
$874$	0.382852	+	2.59896i	0.0129502	+	0.0879111i
$875$	1.24174	+	29.5543i	0.0419784	+	0.999119i
$876$	−0.0157507	−	0.978451i	−0.000532166	−	0.0330588i
$877$	−7.39160	+	27.5858i	−0.249597	+	0.931508i	0.721420	+	0.692497i	$0.243490\pi$
$877$	−7.39160	+	27.5858i	−0.249597	+	0.931508i	−0.971017	+	0.239010i	$0.923177\pi$
$878$	−35.7288	+	15.4464i	−1.20579	+	0.521291i
$879$	−3.80930	+	3.69951i	−0.128485	+	0.124781i
$880$	23.2048	+	11.6309i	0.782232	+	0.392077i
$881$		−	11.2075i		−	0.377591i	−0.982016	−	0.188795i	$-0.939542\pi$
$881$		−	11.2075i		−	0.377591i	0.982016	−	0.188795i	$-0.0604583\pi$
$882$	−29.6670	−	1.36627i	−0.998941	−	0.0460048i
$883$	−30.4725	+	30.4725i	−1.02548	+	1.02548i	−0.0258147	+	0.999667i	$0.508218\pi$
$883$	−30.4725	+	30.4725i	−1.02548	+	1.02548i	−0.999667	+	0.0258147i	$0.991782\pi$
$884$	−13.1993	+	14.0362i	−0.443941	+	0.472087i
$885$	−0.995954	−	0.0170158i	−0.0334786	−	0.000571981i
$886$	3.45612	−	8.72024i	0.116110	−	0.292962i
$887$	−4.36800	+	16.3016i	−0.146663	+	0.547354i	0.853013	+	0.521890i	$0.174773\pi$
$887$	−4.36800	+	16.3016i	−0.146663	+	0.547354i	−0.999676	+	0.0254638i	$0.991894\pi$
$888$	27.6125	+	19.8400i	0.926614	+	0.665786i
$889$	3.93805	+	3.56714i	0.132078	+	0.119638i
$890$	−3.38562	+	4.53205i	−0.113486	+	0.151915i
$891$	−14.3588	+	21.8171i	−0.481037	+	0.730900i
$892$	14.4494	+	23.3409i	0.483800	+	0.781510i
$893$	41.3510	−	11.0800i	1.38376	−	0.370777i
$894$	9.90270	+	23.8574i	0.331196	+	0.797912i
$895$	−0.0885217	+	35.9376i	−0.00295896	+	1.20126i
$896$	20.6089	−	21.7089i	0.688494	−	0.725242i
$897$	−0.297780	−	0.533638i	−0.00994259	−	0.0178177i
$898$	−10.5685	−	1.22657i	−0.352676	−	0.0409310i
$899$	33.2981	+	19.2247i	1.11055	+	0.641179i
$900$	21.2863	−	21.1399i	0.709542	−	0.704663i
$901$	−37.2248	+	21.4917i	−1.24014	+	0.715994i
$902$	16.2001	+	12.0400i	0.539403	+	0.400889i
$903$	−3.65329	+	3.91652i	−0.121574	+	0.130334i
$904$	−20.2808	+	9.51745i	−0.674530	+	0.316546i
$905$	10.7575	−	6.17556i	0.357591	−	0.205283i
$906$	25.3513	+	19.4230i	0.842239	+	0.645286i
$907$	29.5212	−	7.91019i	0.980236	−	0.262653i	0.267092	−	0.963671i	$-0.413937\pi$
$907$	29.5212	−	7.91019i	0.980236	−	0.262653i	0.713144	+	0.701018i	$0.247271\pi$
$908$	1.43610	+	46.7391i	0.0476587	+	1.55109i
$909$	12.0337	−	19.5030i	0.399133	−	0.646874i
$910$	4.35309	−	12.6913i	0.144304	−	0.420712i
$911$		−	30.5070i		−	1.01074i	−0.862902	−	0.505371i	$-0.831356\pi$
$911$		−	30.5070i		−	1.01074i	0.862902	−	0.505371i	$-0.168644\pi$
$912$	58.4317	−	2.73733i	1.93487	−	0.0906421i
$913$	−10.0418	+	2.69070i	−0.332336	+	0.0890491i
$914$	17.0446	+	6.75534i	0.563786	+	0.223447i
$915$	−0.216432	+	0.360505i	−0.00715501	+	0.0119179i
$916$	−14.1126	−	46.8616i	−0.466293	−	1.54835i
$917$	−35.2721	+	22.7568i	−1.16479	+	0.751497i
$918$	−4.51245	−	43.9139i	−0.148933	−	1.44937i
$919$	−32.1087	+	18.5380i	−1.05917	+	0.611511i	−0.925202	−	0.379475i	$-0.876105\pi$
$919$	−32.1087	+	18.5380i	−1.05917	+	0.611511i	−0.133966	+	0.990986i	$0.542771\pi$
$920$	0.121305	−	1.38617i	0.00399930	−	0.0457006i
$921$	23.6605	−	22.9786i	0.779641	−	0.757171i
$922$	−3.09555	−	0.359264i	−0.101946	−	0.0118317i
$923$	−14.6166	−	14.6166i	−0.481111	−	0.481111i
$924$	−17.5364	+	19.9975i	−0.576905	+	0.657869i
$925$	24.4170	+	24.6588i	0.802825	+	0.810775i
$926$	23.0325	+	29.0807i	0.756896	+	0.955652i
$927$	4.26931	−	14.2526i	0.140223	−	0.468118i
$928$	17.4427	−	26.7568i	0.572583	−	0.878334i
$929$	−19.8843	−	34.4407i	−0.652384	−	1.12996i	−0.982543	−	0.186037i	$-0.940436\pi$
$929$	−19.8843	−	34.4407i	−0.652384	−	1.12996i	0.330159	−	0.943925i	$-0.392898\pi$
$930$	4.93219	−	36.9707i	0.161733	−	1.21232i
$931$	−34.4537	−	48.0207i	−1.12918	−	1.57381i
$932$	−50.0905	−	26.9034i	−1.64077	−	0.881251i
$933$	−21.9585	+	36.7807i	−0.718888	+	1.20414i
$934$	21.3612	+	8.46616i	0.698961	+	0.277021i
$935$	37.6791	−	9.99667i	1.23224	−	0.326926i
$936$	−12.4822	+	5.41822i	−0.407993	+	0.177100i
$937$	27.8841	−	27.8841i	0.910935	−	0.910935i	−0.0854105	−	0.996346i	$-0.527220\pi$
$937$	27.8841	−	27.8841i	0.910935	−	0.910935i	0.996346	+	0.0854105i	$0.0272202\pi$
$938$	−10.7774	−	54.3838i	−0.351894	−	1.77569i
$939$	−9.62369	−	2.73007i	−0.314057	−	0.0890923i
$940$	−22.6663	+	0.640561i	−0.739292	+	0.0208928i
$941$	24.3262	−	42.1343i	0.793013	−	1.37354i	−0.131081	−	0.991372i	$-0.541845\pi$
$941$	24.3262	−	42.1343i	0.793013	−	1.37354i	0.924093	−	0.382167i	$-0.124822\pi$
$942$	−7.25911	−	54.8257i	−0.236515	−	1.78632i
$943$	0.280050	−	1.04516i	0.00911968	−	0.0340351i
$944$	0.568112	+	0.857678i	0.0184905	+	0.0279150i
$945$	15.4517	+	26.5752i	0.502645	+	0.864493i
$946$	0.699050	+	4.74544i	0.0227281	+	0.154288i
$947$	3.06215	+	0.820501i	0.0995066	+	0.0266627i	0.308229	−	0.951312i	$-0.400264\pi$
$947$	3.06215	+	0.820501i	0.0995066	+	0.0266627i	−0.208722	+	0.977975i	$0.566930\pi$
$948$	0.701445	+	2.45882i	0.0227819	+	0.0798587i
$949$	−0.226508	+	0.392324i	−0.00735277	+	0.0127354i
$950$	59.2693	+	7.17480i	1.92295	+	0.232781i
$951$	−3.97131	+	13.9992i	−0.128779	+	0.453955i
$952$	1.59310	−	44.9269i	0.0516326	−	1.45609i
$953$	−15.3667	+	15.3667i	−0.497776	+	0.497776i	−0.910745	−	0.412969i	$-0.864492\pi$
$953$	−15.3667	+	15.3667i	−0.497776	+	0.497776i	0.412969	+	0.910745i	$0.364492\pi$
$954$	−30.1489	+	3.54415i	−0.976108	+	0.114746i
$955$	1.94531	+	1.12952i	0.0629487	+	0.0365505i
$956$	−42.7858	−	10.0669i	−1.38379	−	0.325587i
$957$	−14.5481	+	24.3683i	−0.470275	+	0.787715i
$958$	−6.14331	+	8.26594i	−0.198481	+	0.267060i
$959$	10.3225	+	32.0944i	0.333330	+	1.03638i
$960$	−30.4452	−	5.75217i	−0.982616	−	0.185651i
$961$	−7.68599	−	13.3125i	−0.247935	−	0.429436i
$962$	−6.24615	−	14.4479i	−0.201384	−	0.465818i
$963$	−34.1184	−	10.2200i	−1.09945	−	0.329335i
$964$	27.1617	−	28.8837i	0.874818	−	0.930281i
$965$	4.66683	+	4.68988i	0.150230	+	0.150972i
$966$	1.34297	+	0.478962i	0.0432095	+	0.0154104i
$967$	36.4455	−	36.4455i	1.17201	−	1.17201i	0.190276	−	0.981731i	$-0.439062\pi$
$967$	36.4455	−	36.4455i	1.17201	−	1.17201i	0.981731	−	0.190276i	$-0.0609384\pi$
$968$	−1.28385	−	7.17856i	−0.0412645	−	0.230728i
$969$	63.0221	−	61.2057i	2.02456	−	1.96621i
$970$	−32.5894	−	13.0092i	−1.04638	−	0.417701i
$971$	−1.20687	−	2.09037i	−0.0387304	−	0.0670831i	0.846010	−	0.533166i	$-0.178998\pi$
$971$	−1.20687	−	2.09037i	−0.0387304	−	0.0670831i	−0.884741	+	0.466083i	$0.845665\pi$
$972$	9.33793	−	29.7456i	0.299514	−	0.954092i
$973$	1.68086	+	34.0113i	0.0538858	+	1.09035i
$974$	−0.199107	−	1.35162i	−0.00637979	−	0.0433087i
$975$	−13.4825	+	3.33160i	−0.431785	+	0.106697i
$976$	0.433455	−	0.0266618i	0.0138745	−	0.000853422i
$977$	50.9754	−	13.6588i	1.63085	−	0.436984i	0.676685	−	0.736272i	$-0.263416\pi$
$977$	50.9754	−	13.6588i	1.63085	−	0.436984i	0.954163	+	0.299288i	$0.0967492\pi$
$978$	11.9464	−	28.9016i	0.382005	−	0.924170i
$979$	−5.19144			−0.165919
$980$	11.8674	+	28.9683i	0.379090	+	0.925360i
$981$	−1.14655	+	1.85822i	−0.0366066	+	0.0593283i
$982$	35.8302	+	4.15839i	1.14339	+	0.132700i
$983$	14.6183	+	54.5562i	0.466251	+	1.74007i	0.652709	+	0.757608i	$0.273632\pi$
$983$	14.6183	+	54.5562i	0.466251	+	1.74007i	−0.186459	+	0.982463i	$0.559701\pi$
$984$	−22.5386	−	8.51564i	−0.718504	−	0.271469i
$985$	−0.683227	−	0.184875i	−0.0217694	−	0.00589061i
$986$	−6.99087	−	47.4570i	−0.222635	−	1.51134i
$987$	5.23011	−	22.6390i	0.166476	−	0.720607i
$988$	−23.8564	−	12.8132i	−0.758975	−	0.407643i
$989$	0.222687	−	0.128569i	0.00708105	−	0.00408825i
$990$	27.2331	+	4.03917i	0.865524	+	0.128373i
$991$	−20.4571	+	35.4327i	−0.649841	+	1.12556i	0.333319	+	0.942814i	$0.391831\pi$
$991$	−20.4571	+	35.4327i	−0.649841	+	1.12556i	−0.983161	+	0.182744i	$0.941502\pi$
$992$	−34.3534	+	17.4283i	−1.09072	+	0.553350i
$993$	−16.6223	−	29.7882i	−0.527494	−	0.945299i
$994$	48.1243	+	3.18862i	1.52641	+	0.101137i
$995$	−0.0415819	+	16.8812i	−0.00131824	+	0.535170i
$996$	10.6458	−	6.37699i	0.337325	−	0.202063i
$997$	8.51829	−	2.28247i	0.269777	−	0.0722865i	−0.121395	−	0.992604i	$-0.538737\pi$
$997$	8.51829	−	2.28247i	0.269777	−	0.0722865i	0.391171	+	0.920318i	$0.372070\pi$
$998$	9.04709	+	20.9267i	0.286381	+	0.662423i
$999$	34.3920	+	10.8523i	1.08811	+	0.343353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dc.e.53.6	✓	704
3.2	odd	2	inner	840.2.dc.e.53.171	yes	704
5.2	odd	4	inner	840.2.dc.e.557.94	yes	704
7.2	even	3	inner	840.2.dc.e.653.109	yes	704
8.5	even	2	inner	840.2.dc.e.53.156	yes	704
15.2	even	4	inner	840.2.dc.e.557.83	yes	704
21.2	odd	6	inner	840.2.dc.e.653.68	yes	704
24.5	odd	2	inner	840.2.dc.e.53.21	yes	704
35.2	odd	12	inner	840.2.dc.e.317.21	yes	704
40.37	odd	4	inner	840.2.dc.e.557.68	yes	704
56.37	even	6	inner	840.2.dc.e.653.83	yes	704
105.2	even	12	inner	840.2.dc.e.317.156	yes	704
120.77	even	4	inner	840.2.dc.e.557.109	yes	704
168.149	odd	6	inner	840.2.dc.e.653.94	yes	704
280.37	odd	12	inner	840.2.dc.e.317.171	yes	704
840.317	even	12	inner	840.2.dc.e.317.6	yes	704

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dc.e.53.6	✓	704	1.1	even	1	trivial
840.2.dc.e.53.21	yes	704	24.5	odd	2	inner
840.2.dc.e.53.156	yes	704	8.5	even	2	inner
840.2.dc.e.53.171	yes	704	3.2	odd	2	inner
840.2.dc.e.317.6	yes	704	840.317	even	12	inner
840.2.dc.e.317.21	yes	704	35.2	odd	12	inner
840.2.dc.e.317.156	yes	704	105.2	even	12	inner
840.2.dc.e.317.171	yes	704	280.37	odd	12	inner
840.2.dc.e.557.68	yes	704	40.37	odd	4	inner
840.2.dc.e.557.83	yes	704	15.2	even	4	inner
840.2.dc.e.557.94	yes	704	5.2	odd	4	inner
840.2.dc.e.557.109	yes	704	120.77	even	4	inner
840.2.dc.e.653.68	yes	704	21.2	odd	6	inner
840.2.dc.e.653.83	yes	704	56.37	even	6	inner
840.2.dc.e.653.94	yes	704	168.149	odd	6	inner
840.2.dc.e.653.109	yes	704	7.2	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40478 - 0.163037i) q^{2} +(0.0253219 - 1.73187i) q^{3} +(1.94684 + 0.458064i) q^{4} +(-1.11326 - 1.93924i) q^{5} +(-0.317930 + 2.42877i) q^{6} +(0.130595 + 2.64253i) q^{7} +(-2.66021 - 0.960888i) q^{8} +(-2.99872 - 0.0877081i) q^{9} +(1.24772 + 2.90572i) q^{10} +(-1.45101 + 2.51322i) q^{11} +(0.842603 - 3.36006i) q^{12} +(-1.13395 + 1.13395i) q^{13} +(0.247372 - 3.73347i) q^{14} +(-3.38669 + 1.87891i) q^{15} +(3.58035 + 1.78355i) q^{16} +(5.80269 - 1.55483i) q^{17} +(4.19825 + 0.612113i) q^{18} +(4.22157 + 7.31197i) q^{19} +(-1.27904 - 4.28533i) q^{20} +(4.57981 - 0.159259i) q^{21} +(2.44811 - 3.29397i) q^{22} +(-0.212513 - 0.0569428i) q^{23} +(-1.73149 + 4.58279i) q^{24} +(-2.52130 + 4.31776i) q^{25} +(1.77783 - 1.40808i) q^{26} +(-0.227832 + 5.19116i) q^{27} +(-0.956199 + 5.20439i) q^{28} +5.64627i q^{29} +(5.06391 - 2.08731i) q^{30} +(3.40485 - 5.89737i) q^{31} +(-4.73884 - 3.08924i) q^{32} +(4.31582 + 2.57659i) q^{33} +(-8.40502 + 1.23814i) q^{34} +(4.97911 - 3.19508i) q^{35} +(-5.79784 - 1.54436i) q^{36} +(1.79632 - 6.70395i) q^{37} +(-4.73827 - 10.9600i) q^{38} +(1.93514 + 1.99256i) q^{39} +(1.09811 + 6.22850i) q^{40} +4.91810i q^{41} +(-6.45961 - 0.522953i) q^{42} +(-0.826434 + 0.826434i) q^{43} +(-3.97610 + 4.22818i) q^{44} +(3.16827 + 5.91287i) q^{45} +(0.289251 + 0.114640i) q^{46} +(1.31230 - 4.89758i) q^{47} +(3.17953 - 6.15553i) q^{48} +(-6.96589 + 0.690202i) q^{49} +(4.24584 - 5.65445i) q^{50} +(-2.54581 - 10.0889i) q^{51} +(-2.72704 + 1.68820i) q^{52} +(-6.91130 + 1.85188i) q^{53} +(1.16641 - 7.25531i) q^{54} +(6.48910 + 0.0159840i) q^{55} +(2.19176 - 7.15515i) q^{56} +(12.7703 - 7.12604i) q^{57} +(0.920551 - 7.93179i) q^{58} +(0.222735 + 0.128596i) q^{59} +(-7.45400 + 2.10662i) q^{60} +(0.0940230 - 0.0542842i) q^{61} +(-5.74457 + 7.72942i) q^{62} +(-0.159847 - 7.93564i) q^{63} +(6.15339 + 5.11232i) q^{64} +(3.46139 + 0.936620i) q^{65} +(-5.64272 - 4.32320i) q^{66} +(14.3124 - 3.83501i) q^{67} +(12.0091 - 0.368991i) q^{68} +(-0.103998 + 0.366603i) q^{69} +(-7.51549 + 3.67661i) q^{70} +12.8900i q^{71} +(7.89293 + 3.11475i) q^{72} +(0.272865 - 0.0731140i) q^{73} +(-3.61643 + 9.12474i) q^{74} +(7.41393 + 4.47589i) q^{75} +(4.86936 + 16.1690i) q^{76} +(-6.83075 - 3.50612i) q^{77} +(-2.39359 - 3.11462i) q^{78} +(-0.639229 + 0.369059i) q^{79} +(-0.527132 - 8.92873i) q^{80} +(8.98461 + 0.526024i) q^{81} +(0.801832 - 6.90886i) q^{82} +(2.53311 + 2.53311i) q^{83} +(8.98909 + 1.78779i) q^{84} +(-9.47509 - 9.52188i) q^{85} +(1.29570 - 1.02622i) q^{86} +(9.77857 + 0.142974i) q^{87} +(6.27491 - 5.29143i) q^{88} +(0.894453 + 1.54924i) q^{89} +(-3.48671 - 8.82286i) q^{90} +(-3.14458 - 2.84841i) q^{91} +(-0.387645 - 0.208203i) q^{92} +(-10.1272 - 6.04607i) q^{93} +(-2.64199 + 6.66609i) q^{94} +(9.47996 - 16.3268i) q^{95} +(-5.47014 + 8.12881i) q^{96} +(-7.84637 + 7.84637i) q^{97} +(9.89810 + 0.166114i) q^{98} +(4.57160 - 7.40918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 704 q - 16 q^{6} - 24 q^{7} + 12 q^{10} + 10 q^{12} + 32 q^{15} - 72 q^{16} + 6 q^{18} + 64 q^{22} - 8 q^{25} + 24 q^{28} + 8 q^{30} - 16 q^{31} + 44 q^{33} - 240 q^{36} + 16 q^{40} - 78 q^{42} - 8 q^{46}+ \cdots - 80 q^{97}+O(q^{100}) \) 704 * q - 16 * q^6 - 24 * q^7 + 12 * q^10 + 10 * q^12 + 32 * q^15 - 72 * q^16 + 6 * q^18 + 64 * q^22 - 8 * q^25 + 24 * q^28 + 8 * q^30 - 16 * q^31 + 44 * q^33 - 240 * q^36 + 16 * q^40 - 78 * q^42 - 8 * q^46 - 20 * q^48 - 60 * q^52 + 272 * q^55 + 8 * q^57 - 20 * q^58 - 14 * q^60 + 12 * q^63 - 84 * q^66 + 112 * q^70 - 38 * q^72 + 104 * q^73 - 64 * q^76 - 16 * q^78 - 168 * q^81 - 72 * q^82 - 64 * q^87 + 52 * q^88 - 44 * q^90 + 40 * q^96 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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