LMFDB - Embedded newform 143.4.g.a.21.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(21,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("143.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.g (of order $4$, degree $2$, 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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.17
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.629214 + 0.629214i) q^{2} +3.19940 q^{3} +7.20818i q^{4} +(-11.3086 - 11.3086i) q^{5} +(-2.01311 + 2.01311i) q^{6} +(15.7918 + 15.7918i) q^{7} +(-9.56920 - 9.56920i) q^{8} -16.7639 q^{9} +O(q^{10})$	\(q+(-0.629214 + 0.629214i) q^{2} +3.19940 q^{3} +7.20818i q^{4} +(-11.3086 - 11.3086i) q^{5} +(-2.01311 + 2.01311i) q^{6} +(15.7918 + 15.7918i) q^{7} +(-9.56920 - 9.56920i) q^{8} -16.7639 q^{9} +14.2311 q^{10} +(7.12528 + 35.7803i) q^{11} +23.0618i q^{12} +(-24.3375 + 40.0585i) q^{13} -19.8728 q^{14} +(-36.1808 - 36.1808i) q^{15} -45.6233 q^{16} -27.6573 q^{17} +(10.5481 - 10.5481i) q^{18} +(-31.0451 + 31.0451i) q^{19} +(81.5147 - 81.5147i) q^{20} +(50.5241 + 50.5241i) q^{21} +(-26.9968 - 18.0301i) q^{22} -9.14702i q^{23} +(-30.6157 - 30.6157i) q^{24} +130.771i q^{25} +(-9.89186 - 40.5189i) q^{26} -140.018 q^{27} +(-113.830 + 113.830i) q^{28} -11.6020i q^{29} +45.5310 q^{30} +(46.4566 + 46.4566i) q^{31} +(105.260 - 105.260i) q^{32} +(22.7966 + 114.475i) q^{33} +(17.4023 - 17.4023i) q^{34} -357.167i q^{35} -120.837i q^{36} +(-275.748 + 275.748i) q^{37} -39.0681i q^{38} +(-77.8654 + 128.163i) q^{39} +216.429i q^{40} +(-230.425 + 230.425i) q^{41} -63.5809 q^{42} +520.653 q^{43} +(-257.911 + 51.3603i) q^{44} +(189.577 + 189.577i) q^{45} +(5.75543 + 5.75543i) q^{46} +(175.451 - 175.451i) q^{47} -145.967 q^{48} +155.759i q^{49} +(-82.2828 - 82.2828i) q^{50} -88.4865 q^{51} +(-288.749 - 175.429i) q^{52} +286.898 q^{53} +(88.1013 - 88.1013i) q^{54} +(324.049 - 485.204i) q^{55} -302.229i q^{56} +(-99.3257 + 99.3257i) q^{57} +(7.30015 + 7.30015i) q^{58} +(564.939 - 564.939i) q^{59} +(260.798 - 260.798i) q^{60} -354.009i q^{61} -58.4623 q^{62} +(-264.731 - 264.731i) q^{63} -232.524i q^{64} +(728.232 - 177.783i) q^{65} +(-86.3735 - 57.6856i) q^{66} +(240.612 + 240.612i) q^{67} -199.358i q^{68} -29.2649i q^{69} +(224.734 + 224.734i) q^{70} +(254.957 + 254.957i) q^{71} +(160.417 + 160.417i) q^{72} +(791.873 + 791.873i) q^{73} -347.010i q^{74} +418.388i q^{75} +(-223.779 - 223.779i) q^{76} +(-452.513 + 677.554i) q^{77} +(-31.6480 - 129.636i) q^{78} -596.036i q^{79} +(515.937 + 515.937i) q^{80} +4.65131 q^{81} -289.973i q^{82} +(-605.860 + 605.860i) q^{83} +(-364.187 + 364.187i) q^{84} +(312.766 + 312.766i) q^{85} +(-327.602 + 327.602i) q^{86} -37.1194i q^{87} +(274.206 - 410.572i) q^{88} +(60.2408 - 60.2408i) q^{89} -238.568 q^{90} +(-1016.93 + 248.262i) q^{91} +65.9333 q^{92} +(148.633 + 148.633i) q^{93} +220.793i q^{94} +702.157 q^{95} +(336.770 - 336.770i) q^{96} +(-902.850 - 902.850i) q^{97} +(-98.0057 - 98.0057i) q^{98} +(-119.447 - 599.816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.629214	+	0.629214i	−0.222461	+	0.222461i	−0.809534	−	0.587073i	$-0.800280\pi$
$2$	−0.629214	+	0.629214i	−0.222461	+	0.222461i	0.587073	+	0.809534i	$0.300280\pi$
$3$	3.19940			0.615724			0.307862	−	0.951431i	$-0.400386\pi$
$3$	3.19940			0.615724			0.307862	+	0.951431i	$0.400386\pi$
$4$			7.20818i			0.901022i
$5$	−11.3086	−	11.3086i	−1.01148	−	1.01148i	−0.999933	−	0.0115424i	$-0.996326\pi$
$5$	−11.3086	−	11.3086i	−1.01148	−	1.01148i	−0.0115424	−	0.999933i	$-0.503674\pi$
$6$	−2.01311	+	2.01311i	−0.136974	+	0.136974i
$7$	15.7918	+	15.7918i	0.852675	+	0.852675i	0.990462	−	0.137787i	$-0.0439990\pi$
$7$	15.7918	+	15.7918i	0.852675	+	0.852675i	−0.137787	+	0.990462i	$0.543999\pi$
$8$	−9.56920	−	9.56920i	−0.422903	−	0.422903i
$9$	−16.7639			−0.620884
$10$	14.2311			0.450027
$11$	7.12528	+	35.7803i	0.195305	+	0.980743i
$11$	7.12528	+	35.7803i	0.195305	+	0.980743i
$12$			23.0618i			0.554781i
$13$	−24.3375	+	40.0585i	−0.519232	+	0.854633i
$13$	−24.3375	+	40.0585i	−0.519232	+	0.854633i
$14$	−19.8728			−0.379373
$15$	−36.1808	−	36.1808i	−0.622790	−	0.622790i
$16$	−45.6233			−0.712864
$17$	−27.6573			−0.394581			−0.197290	−	0.980345i	$-0.563214\pi$
$17$	−27.6573			−0.394581			−0.197290	+	0.980345i	$0.563214\pi$
$18$	10.5481	−	10.5481i	0.138122	−	0.138122i
$19$	−31.0451	+	31.0451i	−0.374855	+	0.374855i	−0.869242	−	0.494387i	$-0.835393\pi$
$19$	−31.0451	+	31.0451i	−0.374855	+	0.374855i	0.494387	+	0.869242i	$0.335393\pi$
$20$	81.5147	−	81.5147i	0.911362	−	0.911362i
$21$	50.5241	+	50.5241i	0.525012	+	0.525012i
$22$	−26.9968	−	18.0301i	−0.261624	−	0.174729i
$23$		−	9.14702i		−	0.0829254i	−0.999140	−	0.0414627i	$-0.986798\pi$
$23$		−	9.14702i		−	0.0829254i	0.999140	−	0.0414627i	$-0.0132018\pi$
$24$	−30.6157	−	30.6157i	−0.260392	−	0.260392i
$25$			130.771i			1.04617i
$26$	−9.89186	−	40.5189i	−0.0746136	−	0.305631i
$27$	−140.018			−0.998017
$28$	−113.830	+	113.830i	−0.768279	+	0.768279i
$29$		−	11.6020i		−	0.0742910i	−0.999310	−	0.0371455i	$-0.988174\pi$
$29$		−	11.6020i		−	0.0742910i	0.999310	−	0.0371455i	$-0.0118265\pi$
$30$	45.5310			0.277093
$31$	46.4566	+	46.4566i	0.269156	+	0.269156i	0.828760	−	0.559604i	$-0.189047\pi$
$31$	46.4566	+	46.4566i	0.269156	+	0.269156i	−0.559604	+	0.828760i	$0.689047\pi$
$32$	105.260	−	105.260i	0.581487	−	0.581487i
$33$	22.7966	+	114.475i	0.120254	+	0.603867i
$34$	17.4023	−	17.4023i	0.0877787	−	0.0877787i
$35$		−	357.167i		−	1.72492i
$36$		−	120.837i		−	0.559430i
$37$	−275.748	+	275.748i	−1.22521	+	1.22521i	−0.259455	+	0.965755i	$0.583543\pi$
$37$	−275.748	+	275.748i	−1.22521	+	1.22521i	−0.965755	+	0.259455i	$0.916457\pi$
$38$		−	39.0681i		−	0.166781i
$39$	−77.8654	+	128.163i	−0.319704	+	0.526218i
$40$			216.429i			0.855512i
$41$	−230.425	+	230.425i	−0.877715	+	0.877715i	−0.993298	−	0.115583i	$-0.963126\pi$
$41$	−230.425	+	230.425i	−0.877715	+	0.877715i	0.115583	+	0.993298i	$0.463126\pi$
$42$	−63.5809			−0.233589
$43$	520.653			1.84648			0.923242	−	0.384218i	$-0.125529\pi$
$43$	520.653			1.84648			0.923242	+	0.384218i	$0.125529\pi$
$44$	−257.911	+	51.3603i	−0.883671	+	0.175974i
$45$	189.577	+	189.577i	0.628009	+	0.628009i
$46$	5.75543	+	5.75543i	0.0184476	+	0.0184476i
$47$	175.451	−	175.451i	0.544514	−	0.544514i	−0.380335	−	0.924849i	$-0.624191\pi$
$47$	175.451	−	175.451i	0.544514	−	0.544514i	0.924849	+	0.380335i	$0.124191\pi$
$48$	−145.967			−0.438927
$49$			155.759i			0.454108i
$50$	−82.2828	−	82.2828i	−0.232731	−	0.232731i
$51$	−88.4865			−0.242953
$52$	−288.749	−	175.429i	−0.770044	−	0.467840i
$53$	286.898			0.743555			0.371778	−	0.928322i	$-0.378748\pi$
$53$	286.898			0.743555			0.371778	+	0.928322i	$0.378748\pi$
$54$	88.1013	−	88.1013i	0.222020	−	0.222020i
$55$	324.049	−	485.204i	0.794451	−	1.18954i
$56$		−	302.229i		−	0.721197i
$57$	−99.3257	+	99.3257i	−0.230807	+	0.230807i
$58$	7.30015	+	7.30015i	0.0165268	+	0.0165268i
$59$	564.939	−	564.939i	1.24659	−	1.24659i	0.289373	−	0.957216i	$-0.406553\pi$
$59$	564.939	−	564.939i	1.24659	−	1.24659i	0.957216	−	0.289373i	$-0.0934468\pi$
$60$	260.798	−	260.798i	0.561148	−	0.561148i
$61$		−	354.009i		−	0.743053i	−0.928422	−	0.371527i	$-0.878834\pi$
$61$		−	354.009i		−	0.743053i	0.928422	−	0.371527i	$-0.121166\pi$
$62$	−58.4623			−0.119753
$63$	−264.731	−	264.731i	−0.529412	−	0.529412i
$64$		−	232.524i		−	0.454148i
$65$	728.232	−	177.783i	1.38963	−	0.339250i
$66$	−86.3735	−	57.6856i	−0.161088	−	0.107585i
$67$	240.612	+	240.612i	0.438738	+	0.438738i	0.891587	−	0.452849i	$-0.149592\pi$
$67$	240.612	+	240.612i	0.438738	+	0.438738i	−0.452849	+	0.891587i	$0.649592\pi$
$68$		−	199.358i		−	0.355526i
$69$		−	29.2649i		−	0.0510592i
$70$	224.734	+	224.734i	0.383727	+	0.383727i
$71$	254.957	+	254.957i	0.426166	+	0.426166i	0.887320	−	0.461154i	$-0.152564\pi$
$71$	254.957	+	254.957i	0.426166	+	0.426166i	−0.461154	+	0.887320i	$0.652564\pi$
$72$	160.417	+	160.417i	0.262574	+	0.262574i
$73$	791.873	+	791.873i	1.26961	+	1.26961i	0.946289	+	0.323323i	$0.104800\pi$
$73$	791.873	+	791.873i	1.26961	+	1.26961i	0.323323	+	0.946289i	$0.395200\pi$
$74$		−	347.010i		−	0.545122i
$75$			418.388i			0.644150i
$76$	−223.779	−	223.779i	−0.337753	−	0.337753i
$77$	−452.513	+	677.554i	−0.669723	+	1.00279i
$78$	−31.6480	−	129.636i	−0.0459414	−	0.188184i
$79$		−	596.036i		−	0.848852i	−0.905463	−	0.424426i	$-0.860476\pi$
$79$		−	596.036i		−	0.848852i	0.905463	−	0.424426i	$-0.139524\pi$
$80$	515.937	+	515.937i	0.721045	+	0.721045i
$81$	4.65131			0.00638039
$82$		−	289.973i		−	0.390514i
$83$	−605.860	+	605.860i	−0.801226	+	0.801226i	−0.983287	−	0.182061i	$-0.941723\pi$
$83$	−605.860	+	605.860i	−0.801226	+	0.801226i	0.182061	+	0.983287i	$0.441723\pi$
$84$	−364.187	+	364.187i	−0.473048	+	0.473048i
$85$	312.766	+	312.766i	0.399109	+	0.399109i
$86$	−327.602	+	327.602i	−0.410770	+	0.410770i
$87$		−	37.1194i		−	0.0457428i
$88$	274.206	−	410.572i	0.332164	−	0.497354i
$89$	60.2408	−	60.2408i	0.0717473	−	0.0717473i	−0.670323	−	0.742070i	$-0.733844\pi$
$89$	60.2408	−	60.2408i	0.0717473	−	0.0717473i	0.742070	+	0.670323i	$0.233844\pi$
$90$	−238.568			−0.279415
$91$	−1016.93	+	248.262i	−1.17146	+	0.285988i
$92$	65.9333			0.0747177
$93$	148.633	+	148.633i	0.165726	+	0.165726i
$94$			220.793i			0.242266i
$95$	702.157			0.758313
$96$	336.770	−	336.770i	0.358036	−	0.358036i
$97$	−902.850	−	902.850i	−0.945058	−	0.945058i	0.0535098	−	0.998567i	$-0.482959\pi$
$97$	−902.850	−	902.850i	−0.945058	−	0.945058i	−0.998567	+	0.0535098i	$0.982959\pi$
$98$	−98.0057	−	98.0057i	−0.101021	−	0.101021i
$99$	−119.447	−	599.816i	−0.121262	−	0.608927i
$100$	−942.620			−0.942620
$101$	353.462			0.348225			0.174113	−	0.984726i	$-0.444294\pi$
$101$	353.462			0.348225			0.174113	+	0.984726i	$0.444294\pi$
$102$	55.6770	−	55.6770i	0.0540475	−	0.0540475i
$103$		−	766.362i		−	0.733125i	−0.930393	−	0.366563i	$-0.880535\pi$
$103$		−	766.362i		−	0.733125i	0.930393	−	0.366563i	$-0.119465\pi$
$104$	616.219	−	150.437i	0.581012	−	0.141842i
$105$		−	1142.72i		−	1.06207i
$106$	−180.520	+	180.520i	−0.165412	+	0.165412i
$107$			811.693i			0.733358i	0.930348	+	0.366679i	$0.119505\pi$
$107$			811.693i			0.733358i	−0.930348	+	0.366679i	$0.880495\pi$
$108$		−	1009.27i		−	0.899236i
$109$	−999.663	+	999.663i	−0.878444	+	0.878444i	−0.993374	−	0.114930i	$-0.963336\pi$
$109$	−999.663	+	999.663i	−0.878444	+	0.878444i	0.114930	+	0.993374i	$0.463336\pi$
$110$	101.401	+	509.194i	0.0878925	+	0.441361i
$111$	−882.229	+	882.229i	−0.754391	+	0.754391i
$112$	−720.472	−	720.472i	−0.607841	−	0.607841i
$113$	−964.051			−0.802569			−0.401284	−	0.915954i	$-0.631436\pi$
$113$	−964.051			−0.802569			−0.401284	+	0.915954i	$0.631436\pi$
$114$		−	124.994i		−	0.102691i
$115$	−103.440	+	103.440i	−0.0838771	+	0.0838771i
$116$	83.6293			0.0669378
$117$	407.991	−	671.535i	0.322383	−	0.530628i
$118$			710.935i			0.554634i
$119$	−436.757	−	436.757i	−0.336449	−	0.336449i
$120$			692.443i			0.526759i
$121$	−1229.46	+	509.889i	−0.923712	+	0.383088i
$122$	222.748	+	222.748i	0.165300	+	0.165300i
$123$	−737.221	+	737.221i	−0.540430	+	0.540430i
$124$	−334.867	+	334.867i	−0.242516	+	0.242516i
$125$	65.2604	−	65.2604i	0.0466965	−	0.0466965i
$126$	333.145			0.235547
$127$	412.953			0.288533			0.144266	−	0.989539i	$-0.453918\pi$
$127$	412.953			0.288533			0.144266	+	0.989539i	$0.453918\pi$
$128$	988.390	+	988.390i	0.682517	+	0.682517i
$129$	1665.78			1.13693
$130$	−346.350	+	570.077i	−0.233669	+	0.384608i
$131$			699.844i			0.466760i	0.972386	+	0.233380i	$0.0749787\pi$
$131$			699.844i			0.466760i	−0.972386	+	0.233380i	$0.925021\pi$
$132$	−825.159	+	164.322i	−0.544098	+	0.108351i
$133$	−980.514			−0.639259
$134$	−302.793			−0.195204
$135$	1583.41	+	1583.41i	1.00947	+	1.00947i
$136$	264.658	+	264.658i	0.166869	+	0.166869i
$137$	−1311.91	+	1311.91i	−0.818129	+	0.818129i	−0.985837	−	0.167708i	$-0.946363\pi$
$137$	−1311.91	+	1311.91i	−0.818129	+	0.818129i	0.167708	+	0.985837i	$0.446363\pi$
$138$	18.4139	+	18.4139i	0.0113587	+	0.0113587i
$139$			202.971i			0.123855i	0.998081	+	0.0619273i	$0.0197247\pi$
$139$			202.971i			0.123855i	−0.998081	+	0.0619273i	$0.980275\pi$
$140$	2574.52			1.55419
$141$	561.338	−	561.338i	0.335271	−	0.335271i
$142$	−320.845			−0.189610
$143$	−1606.72	−	585.376i	−0.939584	−	0.342319i
$144$	764.822			0.442606
$145$	−131.203	+	131.203i	−0.0751435	+	0.0751435i
$146$	−996.515			−0.564878
$147$			498.335i			0.279605i
$148$	−1987.64	−	1987.64i	−1.10394	−	1.10394i
$149$	1445.97	−	1445.97i	0.795021	−	0.795021i	−0.187285	−	0.982306i	$-0.559969\pi$
$149$	1445.97	−	1445.97i	0.795021	−	0.795021i	0.982306	+	0.187285i	$0.0599687\pi$
$150$	−263.255	−	263.255i	−0.143298	−	0.143298i
$151$	2258.64	+	2258.64i	1.21726	+	1.21726i	0.968589	+	0.248666i	$0.0799922\pi$
$151$	2258.64	+	2258.64i	1.21726	+	1.21726i	0.248666	+	0.968589i	$0.420008\pi$
$152$	594.154			0.317054
$153$	463.642			0.244989
$154$	−141.599	−	711.054i	−0.0740934	−	0.372067i
$155$		−	1050.72i		−	0.544490i
$156$	−923.822	−	561.268i	−0.474135	−	0.288060i
$157$	2180.65			1.10850			0.554250	−	0.832350i	$-0.313005\pi$
$157$	2180.65			1.10850			0.554250	+	0.832350i	$0.313005\pi$
$158$	375.034	+	375.034i	0.188836	+	0.188836i
$159$	917.900			0.457825
$160$	−2380.70			−1.17632
$161$	144.447	−	144.447i	0.0707084	−	0.0707084i
$162$	−2.92667	+	2.92667i	−0.00141939	+	0.00141939i
$163$	−1696.84	+	1696.84i	−0.815380	+	0.815380i	−0.985435	−	0.170055i	$-0.945605\pi$
$163$	−1696.84	+	1696.84i	−0.815380	+	0.815380i	0.170055	+	0.985435i	$0.445605\pi$
$164$	−1660.94	−	1660.94i	−0.790841	−	0.790841i
$165$	1036.76	−	1552.36i	0.489163	−	0.732431i
$166$		−	762.431i		−	0.356483i
$167$	1069.54	+	1069.54i	0.495587	+	0.495587i	0.910061	−	0.414474i	$-0.136034\pi$
$167$	1069.54	+	1069.54i	0.495587	+	0.495587i	−0.414474	+	0.910061i	$0.636034\pi$
$168$		−	966.950i		−	0.444058i
$169$	−1012.37	−	1949.85i	−0.460796	−	0.887506i
$170$	−393.594			−0.177572
$171$	520.436	−	520.436i	0.232741	−	0.232741i
$172$			3752.96i			1.66372i
$173$	−850.654			−0.373838			−0.186919	−	0.982375i	$-0.559850\pi$
$173$	−850.654			−0.373838			−0.186919	+	0.982375i	$0.559850\pi$
$174$	23.3561	+	23.3561i	0.0101760	+	0.0101760i
$175$	−2065.10	+	2065.10i	−0.892040	+	0.892040i
$176$	−325.079	−	1632.42i	−0.139226	−	0.699136i
$177$	1807.46	−	1807.46i	0.767555	−	0.767555i
$178$			75.8087i			0.0319219i
$179$		−	2465.50i		−	1.02950i	−0.857341	−	0.514749i	$-0.827885\pi$
$179$		−	2465.50i		−	1.02950i	0.857341	−	0.514749i	$-0.172115\pi$
$180$	−1366.50	+	1366.50i	−0.565850	+	0.565850i
$181$			1558.63i			0.640066i	0.947406	+	0.320033i	$0.103694\pi$
$181$			1558.63i			0.640066i	−0.947406	+	0.320033i	$0.896306\pi$
$182$	483.655	−	796.074i	0.196983	−	0.324225i
$183$		−	1132.62i		−	0.457516i
$184$	−87.5296	+	87.5296i	−0.0350694	+	0.0350694i
$185$	6236.68			2.47854
$186$	−187.044			−0.0737351
$187$	−197.066	−	989.585i	−0.0770635	−	0.386982i
$188$	1264.68	+	1264.68i	0.490620	+	0.490620i
$189$	−2211.13	−	2211.13i	−0.850984	−	0.850984i
$190$	−441.807	+	441.807i	−0.168695	+	0.168695i
$191$	−919.999			−0.348528			−0.174264	−	0.984699i	$-0.555755\pi$
$191$	−919.999			−0.348528			−0.174264	+	0.984699i	$0.555755\pi$
$192$		−	743.935i		−	0.279630i
$193$	−2397.04	−	2397.04i	−0.894003	−	0.894003i	0.100894	−	0.994897i	$-0.467830\pi$
$193$	−2397.04	−	2397.04i	−0.894003	−	0.894003i	−0.994897	+	0.100894i	$0.967830\pi$
$194$	1136.17			0.420476
$195$	2329.90	−	568.798i	0.855630	−	0.208885i
$196$	−1122.74			−0.409161
$197$	−1936.82	+	1936.82i	−0.700472	+	0.700472i	−0.964512	−	0.264040i	$-0.914945\pi$
$197$	−1936.82	+	1936.82i	−0.700472	+	0.700472i	0.264040	+	0.964512i	$0.414945\pi$
$198$	452.571	+	302.255i	0.162438	+	0.108486i
$199$			3415.41i			1.21664i	0.793691	+	0.608322i	$0.208157\pi$
$199$			3415.41i			1.21664i	−0.793691	+	0.608322i	$0.791843\pi$
$200$	1251.37	−	1251.37i	0.442427	−	0.442427i
$201$	769.814	+	769.814i	0.270142	+	0.270142i
$202$	−222.403	+	222.403i	−0.0774664	+	0.0774664i
$203$	183.216	−	183.216i	0.0633460	−	0.0633460i
$204$		−	637.827i		−	0.218906i
$205$	5211.59			1.77558
$206$	482.206	+	482.206i	0.163092	+	0.163092i
$207$			153.339i			0.0514870i
$208$	1110.36	−	1827.60i	0.370142	−	0.609237i
$209$	−1332.01	−	889.599i	−0.440847	−	0.294425i
$210$	719.014	+	719.014i	0.236270	+	0.236270i
$211$			3026.72i			0.987524i	0.869597	+	0.493762i	$0.164379\pi$
$211$			3026.72i			0.987524i	−0.869597	+	0.493762i	$0.835621\pi$
$212$			2068.01i			0.669960i
$213$	815.707	+	815.707i	0.262401	+	0.262401i
$214$	−510.729	−	510.729i	−0.163143	−	0.163143i
$215$	−5887.88	−	5887.88i	−1.86767	−	1.86767i
$216$	1339.86	+	1339.86i	0.422064	+	0.422064i
$217$			1467.26i			0.459006i
$218$		−	1258.00i		−	0.390838i
$219$	2533.51	+	2533.51i	0.781731	+	0.781731i
$220$	3497.44	+	2335.81i	1.07181	+	0.715818i
$221$	673.110	−	1107.91i	0.204879	−	0.337222i
$222$		−	1110.22i		−	0.335645i
$223$	−1857.64	−	1857.64i	−0.557832	−	0.557832i	0.370858	−	0.928690i	$-0.379064\pi$
$223$	−1857.64	−	1857.64i	−0.557832	−	0.557832i	−0.928690	+	0.370858i	$0.879064\pi$
$224$	3324.49			0.991638
$225$		−	2192.22i		−	0.649548i
$226$	606.594	−	606.594i	0.178540	−	0.178540i
$227$	3995.04	−	3995.04i	1.16811	−	1.16811i	0.185454	−	0.982653i	$-0.440625\pi$
$227$	3995.04	−	3995.04i	1.16811	−	1.16811i	0.982653	−	0.185454i	$-0.0593754\pi$
$228$	−715.958	−	715.958i	−0.207963	−	0.207963i
$229$	1405.97	−	1405.97i	0.405717	−	0.405717i	−0.474525	−	0.880242i	$-0.657380\pi$
$229$	1405.97	−	1405.97i	0.405717	−	0.405717i	0.880242	+	0.474525i	$0.157380\pi$
$230$		−	130.172i		−	0.0373187i
$231$	−1447.77	+	2167.77i	−0.412364	+	0.617439i
$232$	−111.022	+	111.022i	−0.0314179	+	0.0314179i
$233$	−6096.21			−1.71406			−0.857030	−	0.515266i	$-0.827693\pi$
$233$	−6096.21			−1.71406			−0.857030	+	0.515266i	$0.827693\pi$
$234$	165.826	+	679.253i	0.0463264	+	0.189761i
$235$	−3968.23			−1.10153
$236$	4072.18	+	4072.18i	1.12321	+	1.12321i
$237$		−	1906.96i		−	0.522659i
$238$	549.627			0.149693
$239$	−4741.08	+	4741.08i	−1.28316	+	1.28316i	−0.344297	+	0.938861i	$0.611883\pi$
$239$	−4741.08	+	4741.08i	−1.28316	+	1.28316i	−0.938861	+	0.344297i	$0.888117\pi$
$240$	1650.69	+	1650.69i	0.443965	+	0.443965i
$241$	−1504.32	−	1504.32i	−0.402081	−	0.402081i	0.476885	−	0.878966i	$-0.341766\pi$
$241$	−1504.32	−	1504.32i	−0.402081	−	0.402081i	−0.878966	+	0.476885i	$0.841766\pi$
$242$	452.764	−	1094.42i	0.120268	−	0.290712i
$243$	3795.37			1.00195
$244$	2551.76			0.669508
$245$	1761.42	−	1761.42i	0.459319	−	0.459319i
$246$		−	927.739i		−	0.240449i
$247$	−488.060	−	1999.18i	−0.125727	−	0.515000i
$248$		−	889.105i		−	0.227654i
$249$	−1938.39	+	1938.39i	−0.493334	+	0.493334i
$250$			82.1255i			0.0207763i
$251$		−	2325.56i		−	0.584813i	−0.956294	−	0.292407i	$-0.905544\pi$
$251$		−	2325.56i		−	0.584813i	0.956294	−	0.292407i	$-0.0944561\pi$
$252$	1908.23	−	1908.23i	0.477012	−	0.477012i
$253$	327.283	−	65.1751i	0.0813285	−	0.0161957i
$254$	−259.836	+	259.836i	−0.0641872	+	0.0641872i
$255$	1000.66	+	1000.66i	0.245741	+	0.245741i
$256$	616.371			0.150481
$257$		−	4574.54i		−	1.11032i	−0.831744	−	0.555160i	$-0.812657\pi$
$257$		−	4574.54i		−	1.11032i	0.831744	−	0.555160i	$-0.187343\pi$
$258$	−1048.13	+	1048.13i	−0.252921	+	0.252921i
$259$	−8709.10			−2.08941
$260$	1281.49	+	5249.23i	0.305672	+	1.25209i
$261$			194.494i			0.0461261i
$262$	−440.351	−	440.351i	−0.103836	−	0.103836i
$263$		−	2471.84i		−	0.579544i	−0.957096	−	0.289772i	$-0.906420\pi$
$263$		−	2471.84i		−	0.579544i	0.957096	−	0.289772i	$-0.0935795\pi$
$264$	877.293	−	1313.58i	0.204521	−	0.306233i
$265$	−3244.42	−	3244.42i	−0.752088	−	0.752088i
$266$	616.953	−	616.953i	0.142210	−	0.142210i
$267$	192.734	−	192.734i	0.0441766	−	0.0441766i
$268$	−1734.38	+	1734.38i	−0.395313	+	0.395313i
$269$	4287.62			0.971824			0.485912	−	0.874008i	$-0.338488\pi$
$269$	4287.62			0.971824			0.485912	+	0.874008i	$0.338488\pi$
$270$	−1992.61			−0.449135
$271$	4388.23	+	4388.23i	0.983638	+	0.983638i	0.999868	−	0.0162306i	$-0.00516659\pi$
$271$	4388.23	+	4388.23i	0.983638	+	0.983638i	−0.0162306	+	0.999868i	$0.505167\pi$
$272$	1261.82			0.281282
$273$	−3253.55	+	794.288i	−0.721296	+	0.176090i
$274$		−	1650.94i		−	0.364003i
$275$	−4679.02	+	931.779i	−1.02602	+	0.204321i
$276$	210.947			0.0460055
$277$	4287.91			0.930092			0.465046	−	0.885286i	$-0.346038\pi$
$277$	4287.91			0.930092			0.465046	+	0.885286i	$0.346038\pi$
$278$	−127.712	−	127.712i	−0.0275528	−	0.0275528i
$279$	−778.792	−	778.792i	−0.167115	−	0.167115i
$280$	−3417.80	+	3417.80i	−0.729473	+	0.729473i
$281$	1381.97	+	1381.97i	0.293387	+	0.293387i	0.838417	−	0.545030i	$-0.183482\pi$
$281$	1381.97	+	1381.97i	0.293387	+	0.293387i	−0.545030	+	0.838417i	$0.683482\pi$
$282$			706.403i			0.149169i
$283$	5877.82			1.23463			0.617315	−	0.786716i	$-0.288221\pi$
$283$	5877.82			1.23463			0.617315	+	0.786716i	$0.288221\pi$
$284$	−1837.77	+	1837.77i	−0.383985	+	0.383985i
$285$	2246.48			0.466912
$286$	1379.30	−	642.642i	0.285173	−	0.132868i
$287$	−7277.63			−1.49681
$288$	−1764.57	+	1764.57i	−0.361036	+	0.361036i
$289$	−4148.08			−0.844306
$290$		−	165.109i		−	0.0334330i
$291$	−2888.58	−	2888.58i	−0.581895	−	0.581895i
$292$	−5707.96	+	5707.96i	−1.14395	+	1.14395i
$293$	1569.28	+	1569.28i	0.312895	+	0.312895i	0.846030	−	0.533135i	$-0.178986\pi$
$293$	1569.28	+	1569.28i	0.312895	+	0.312895i	−0.533135	+	0.846030i	$0.678986\pi$
$294$	−313.559	−	313.559i	−0.0622012	−	0.0622012i
$295$	−12777.4			−2.52179
$296$	5277.38			1.03629
$297$	−997.667	−	5009.89i	−0.194918	−	0.978798i
$298$			1819.64i			0.353722i
$299$	366.416	+	222.616i	0.0708708	+	0.0430575i
$300$	−3015.81			−0.580394
$301$	8222.02	+	8222.02i	1.57445	+	1.57445i
$302$	−2842.34			−0.541583
$303$	1130.86			0.214411
$304$	1416.38	−	1416.38i	0.267221	−	0.267221i
$305$	−4003.37	+	4003.37i	−0.751580	+	0.751580i
$306$	−291.730	+	291.730i	−0.0545004	+	0.0545004i
$307$	3407.70	+	3407.70i	0.633511	+	0.633511i	0.948947	−	0.315436i	$-0.102151\pi$
$307$	3407.70	+	3407.70i	0.633511	+	0.633511i	−0.315436	+	0.948947i	$0.602151\pi$
$308$	−4883.93	−	3261.80i	−0.903532	−	0.603435i
$309$		−	2451.90i		−	0.451403i
$310$	661.129	+	661.129i	0.121128	+	0.121128i
$311$			7660.95i			1.39682i	0.715696	+	0.698412i	$0.246110\pi$
$311$			7660.95i			1.39682i	−0.715696	+	0.698412i	$0.753890\pi$
$312$	1971.53	−	481.308i	0.357743	−	0.0873356i
$313$	5182.57			0.935898			0.467949	−	0.883756i	$-0.344993\pi$
$313$	5182.57			0.935898			0.467949	+	0.883756i	$0.344993\pi$
$314$	−1372.09	+	1372.09i	−0.246598	+	0.246598i
$315$			5987.49i			1.07097i
$316$	4296.34			0.764835
$317$	4820.75	+	4820.75i	0.854133	+	0.854133i	0.990639	−	0.136507i	$-0.0435875\pi$
$317$	4820.75	+	4820.75i	0.854133	+	0.854133i	−0.136507	+	0.990639i	$0.543587\pi$
$318$	−577.555	+	577.555i	−0.101848	+	0.101848i
$319$	415.123	−	82.6676i	0.0728603	−	0.0145094i
$320$	−2629.53	+	2629.53i	−0.459359	+	0.459359i
$321$			2596.93i			0.451546i
$322$			181.777i			0.0314597i
$323$	858.624	−	858.624i	0.147911	−	0.147911i
$324$			33.5275i			0.00574888i
$325$	−5238.49	−	3182.64i	−0.894089	−	0.543203i
$326$		−	2135.35i		−	0.362780i
$327$	−3198.32	+	3198.32i	−0.540879	+	0.540879i
$328$	4409.96			0.742376
$329$	5541.36			0.928587
$330$	324.421	+	1629.11i	0.0541175	+	0.271757i
$331$	1269.25	+	1269.25i	0.210768	+	0.210768i	0.804594	−	0.593825i	$-0.202383\pi$
$331$	1269.25	+	1269.25i	0.210768	+	0.210768i	−0.593825	+	0.804594i	$0.702383\pi$
$332$	−4367.15	−	4367.15i	−0.721922	−	0.721922i
$333$	4622.61	−	4622.61i	0.760713	−	0.760713i
$334$	−1345.93			−0.220498
$335$		−	5441.99i		−	0.887546i
$336$	−2305.07	−	2305.07i	−0.374262	−	0.374262i
$337$	−7242.68			−1.17072			−0.585362	−	0.810772i	$-0.699048\pi$
$337$	−7242.68			−1.17072			−0.585362	+	0.810772i	$0.699048\pi$
$338$	1863.87	+	589.877i	0.299944	+	0.0949262i
$339$	−3084.38			−0.494161
$340$	−2254.47	+	2254.47i	−0.359606	+	0.359606i
$341$	−1331.21	+	1993.25i	−0.211406	+	0.316541i
$342$			654.932i			0.103552i
$343$	2956.86	−	2956.86i	0.465468	−	0.465468i
$344$	−4982.23	−	4982.23i	−0.780884	−	0.780884i
$345$	−330.947	+	330.947i	−0.0516451	+	0.0516451i
$346$	535.243	−	535.243i	0.0831643	−	0.0831643i
$347$		−	5949.19i		−	0.920373i	−0.887822	−	0.460187i	$-0.847783\pi$
$347$		−	5949.19i		−	0.920373i	0.887822	−	0.460187i	$-0.152217\pi$
$348$	267.563			0.0412152
$349$	−4952.06	−	4952.06i	−0.759534	−	0.759534i	0.216703	−	0.976238i	$-0.430470\pi$
$349$	−4952.06	−	4952.06i	−0.759534	−	0.759534i	−0.976238	+	0.216703i	$0.930470\pi$
$350$		−	2598.78i		−	0.396888i
$351$	3407.69	−	5608.91i	0.518203	−	0.852939i
$352$	4516.26	+	3016.24i	0.683856	+	0.456722i
$353$	−1081.69	−	1081.69i	−0.163096	−	0.163096i	0.620841	−	0.783937i	$-0.286791\pi$
$353$	−1081.69	−	1081.69i	−0.163096	−	0.163096i	−0.783937	+	0.620841i	$0.786791\pi$
$354$			2274.56i			0.341502i
$355$		−	5766.43i		−	0.862113i
$356$	434.226	+	434.226i	0.0646459	+	0.0646459i
$357$	−1397.36	−	1397.36i	−0.207160	−	0.207160i
$358$	1551.33	+	1551.33i	0.229023	+	0.229023i
$359$	5138.83	+	5138.83i	0.755479	+	0.755479i	0.975496	−	0.220017i	$-0.0706114\pi$
$359$	5138.83	+	5138.83i	0.755479	+	0.755479i	−0.220017	+	0.975496i	$0.570611\pi$
$360$		−	3628.19i		−	0.531174i
$361$			4931.40i			0.718968i
$362$	−980.712	−	980.712i	−0.142390	−	0.142390i
$363$	−3933.53	+	1631.34i	−0.568752	+	0.235876i
$364$	−1789.52	−	7330.19i	−0.257682	−	1.05551i
$365$		−	17910.0i		−	2.56836i
$366$	712.658	+	712.658i	0.101779	+	0.101779i
$367$	−2028.34			−0.288497			−0.144248	−	0.989542i	$-0.546076\pi$
$367$	−2028.34			−0.288497			−0.144248	+	0.989542i	$0.546076\pi$
$368$			417.317i			0.0591145i
$369$	3862.81	−	3862.81i	0.544959	−	0.544959i
$370$	−3924.21	+	3924.21i	−0.551378	+	0.551378i
$371$	4530.62	+	4530.62i	0.634011	+	0.634011i
$372$	−1071.37	+	1071.37i	−0.149323	+	0.149323i
$373$		−	7238.79i		−	1.00485i	−0.864620	−	0.502427i	$-0.832441\pi$
$373$		−	7238.79i		−	1.00485i	0.864620	−	0.502427i	$-0.167559\pi$
$374$	746.657	+	498.664i	0.103232	+	0.0689447i
$375$	208.794	−	208.794i	0.0287522	−	0.0287522i
$376$	−3357.85			−0.460553
$377$	464.759	+	282.364i	0.0634915	+	0.0385743i
$378$	2782.55			0.378621
$379$	5459.33	+	5459.33i	0.739913	+	0.739913i	0.972561	−	0.232648i	$-0.0747389\pi$
$379$	5459.33	+	5459.33i	0.739913	+	0.739913i	−0.232648	+	0.972561i	$0.574739\pi$
$380$			5061.27i			0.683257i
$381$	1321.20			0.177657
$382$	578.876	−	578.876i	0.0775337	−	0.0775337i
$383$	3979.28	+	3979.28i	0.530892	+	0.530892i	0.920838	−	0.389946i	$-0.127506\pi$
$383$	3979.28	+	3979.28i	0.530892	+	0.530892i	−0.389946	+	0.920838i	$0.627506\pi$
$384$	3162.25	+	3162.25i	0.420242	+	0.420242i
$385$	12779.5	−	2544.91i	1.69170	−	0.336885i
$386$	3016.50			0.397761
$387$	−8728.16			−1.14645
$388$	6507.91	−	6507.91i	0.851518	−	0.851518i
$389$			7461.94i			0.972585i	0.873796	+	0.486292i	$0.161651\pi$
$389$			7461.94i			0.972585i	−0.873796	+	0.486292i	$0.838349\pi$
$390$	−1108.11	+	1823.90i	−0.143875	+	0.236813i
$391$			252.981i			0.0327208i
$392$	1490.49	−	1490.49i	0.192043	−	0.192043i
$393$			2239.08i			0.287396i
$394$		−	2437.35i		−	0.311655i
$395$	−6740.36	+	6740.36i	−0.858593	+	0.858593i
$396$	4323.58	−	860.997i	0.548657	−	0.109259i
$397$	−3118.00	+	3118.00i	−0.394177	+	0.394177i	−0.876173	−	0.481997i	$-0.839912\pi$
$397$	−3118.00	+	3118.00i	−0.394177	+	0.394177i	0.481997	+	0.876173i	$0.339912\pi$
$398$	−2149.02	−	2149.02i	−0.270655	−	0.270655i
$399$	−3137.05			−0.393607
$400$		−	5966.20i		−	0.745774i
$401$	−6654.33	+	6654.33i	−0.828681	+	0.828681i	−0.987334	−	0.158653i	$-0.949285\pi$
$401$	−6654.33	+	6654.33i	−0.828681	+	0.828681i	0.158653	+	0.987334i	$0.449285\pi$
$402$	−968.755			−0.120192
$403$	−2991.62	+	730.343i	−0.369785	+	0.0902754i
$404$			2547.81i			0.313759i
$405$	−52.6000	−	52.6000i	−0.00645361	−	0.00645361i
$406$			230.564i			0.0281840i
$407$	−11831.2	−	7901.58i	−1.44091	−	0.962326i
$408$	846.745	+	846.745i	0.102745	+	0.102745i
$409$	−82.1740	+	82.1740i	−0.00993458	+	0.00993458i	−0.712057	−	0.702122i	$-0.752236\pi$
$409$	−82.1740	+	82.1740i	−0.00993458	+	0.00993458i	0.702122	+	0.712057i	$0.252236\pi$
$410$	−3279.20	+	3279.20i	−0.394996	+	0.394996i
$411$	−4197.31	+	4197.31i	−0.503742	+	0.503742i
$412$	5524.08			0.660562
$413$	17842.8			2.12587
$414$	−96.4832	−	96.4832i	−0.0114538	−	0.0114538i
$415$	13702.9			1.62084
$416$	1654.80	+	6778.35i	0.195031	+	0.798885i
$417$			649.386i			0.0762603i
$418$	1397.87	−	278.371i	0.163569	−	0.0325731i
$419$	4393.78			0.512292			0.256146	−	0.966638i	$-0.417547\pi$
$419$	4393.78			0.512292			0.256146	+	0.966638i	$0.417547\pi$
$420$	8236.91			0.956953
$421$	11471.2	+	11471.2i	1.32796	+	1.32796i	0.907151	+	0.420806i	$0.138253\pi$
$421$	11471.2	+	11471.2i	1.32796	+	1.32796i	0.420806	+	0.907151i	$0.361747\pi$
$422$	−1904.45	−	1904.45i	−0.219685	−	0.219685i
$423$	−2941.24	+	2941.24i	−0.338080	+	0.338080i
$424$	−2745.38	−	2745.38i	−0.314452	−	0.314452i
$425$		−	3616.76i		−	0.412797i
$426$	−1026.51			−0.116748
$427$	5590.43	−	5590.43i	0.633583	−	0.633583i
$428$	−5850.83			−0.660772
$429$	−5140.53	−	1872.85i	−0.578524	−	0.210774i
$430$	7409.47			0.830969
$431$	563.853	−	563.853i	0.0630159	−	0.0630159i	−0.674896	−	0.737912i	$-0.735812\pi$
$431$	563.853	−	563.853i	0.0630159	−	0.0630159i	0.737912	+	0.674896i	$0.235812\pi$
$432$	6388.08			0.711450
$433$		−	4284.09i		−	0.475474i	−0.971330	−	0.237737i	$-0.923594\pi$
$433$		−	4284.09i		−	0.475474i	0.971330	−	0.237737i	$-0.0764056\pi$
$434$	−923.222	−	923.222i	−0.102111	−	0.102111i
$435$	−419.770	+	419.770i	−0.0462677	+	0.0462677i
$436$	−7205.75	−	7205.75i	−0.791497	−	0.791497i
$437$	283.970	+	283.970i	0.0310850	+	0.0310850i
$438$	−3188.25			−0.347809
$439$	−10076.4			−1.09549			−0.547744	−	0.836646i	$-0.684513\pi$
$439$	−10076.4			−1.09549			−0.547744	+	0.836646i	$0.684513\pi$
$440$	−7743.91	+	1542.12i	−0.839037	+	0.167086i
$441$		−	2611.12i		−	0.281948i
$442$	273.582	+	1120.64i	0.0294411	+	0.120596i
$443$	−7017.70			−0.752643			−0.376321	−	0.926489i	$-0.622811\pi$
$443$	−7017.70			−0.752643			−0.376321	+	0.926489i	$0.622811\pi$
$444$	−6359.26	−	6359.26i	−0.679724	−	0.679724i
$445$	−1362.48			−0.145141
$446$	2337.70			0.248191
$447$	4626.22	−	4626.22i	0.489514	−	0.489514i
$448$	3671.96	−	3671.96i	0.387240	−	0.387240i
$449$	13060.4	−	13060.4i	1.37274	−	1.37274i	0.516374	−	0.856363i	$-0.327282\pi$
$449$	13060.4	−	13060.4i	1.37274	−	1.37274i	0.856363	−	0.516374i	$-0.172718\pi$
$450$	1379.38	+	1379.38i	0.144499	+	0.144499i
$451$	−9886.51	−	6602.83i	−1.03223	−	0.689391i
$452$		−	6949.05i		−	0.723133i
$453$	7226.29	+	7226.29i	0.749494	+	0.749494i
$454$			5027.47i			0.519716i
$455$	14307.6	+	8692.55i	1.47417	+	0.895634i
$456$	1900.94			0.195218
$457$	661.284	−	661.284i	0.0676883	−	0.0676883i	−0.672452	−	0.740141i	$-0.734759\pi$
$457$	661.284	−	661.284i	0.0676883	−	0.0676883i	0.740141	+	0.672452i	$0.234759\pi$
$458$			1769.31i			0.180512i
$459$	3872.51			0.393798
$460$	−745.616	−	745.616i	−0.0755751	−	0.0755751i
$461$	5386.62	−	5386.62i	0.544208	−	0.544208i	−0.380551	−	0.924760i	$-0.624266\pi$
$461$	5386.62	−	5386.62i	0.544208	−	0.544208i	0.924760	+	0.380551i	$0.124266\pi$
$462$	−453.032	−	2274.94i	−0.0456211	−	0.229091i
$463$	2383.10	−	2383.10i	0.239205	−	0.239205i	−0.577316	−	0.816521i	$-0.695900\pi$
$463$	2383.10	−	2383.10i	0.239205	−	0.239205i	0.816521	+	0.577316i	$0.195900\pi$
$464$			529.322i			0.0529594i
$465$		−	3361.68i		−	0.335256i
$466$	3835.82	−	3835.82i	0.381311	−	0.381311i
$467$		−	18733.5i		−	1.85628i	−0.372230	−	0.928141i	$-0.621407\pi$
$467$		−	18733.5i		−	1.85628i	0.372230	−	0.928141i	$-0.378593\pi$
$468$	4840.55	+	2940.87i	0.478108	+	0.290474i
$469$			7599.38i			0.748202i
$470$	2496.86	−	2496.86i	0.245046	−	0.245046i
$471$	6976.75			0.682530
$472$	−10812.0			−1.05437
$473$	3709.80	+	18629.1i	0.360627	+	1.81093i
$474$	1199.88	+	1199.88i	0.116271	+	0.116271i
$475$	−4059.80	−	4059.80i	−0.392161	−	0.392161i
$476$	3148.22	−	3148.22i	0.303148	−	0.303148i
$477$	−4809.51			−0.461661
$478$		−	5966.30i		−	0.570904i
$479$	11666.8	+	11666.8i	1.11288	+	1.11288i	0.992760	+	0.120117i	$0.0383271\pi$
$479$	11666.8	+	11666.8i	1.11288	+	1.11288i	0.120117	+	0.992760i	$0.461673\pi$
$480$	−7616.82			−0.724289
$481$	−4335.04	−	17757.1i	−0.410937	−	1.68327i
$482$	1893.07			0.178894
$483$	462.145	−	462.145i	0.0435369	−	0.0435369i
$484$	−3675.37	−	8862.17i	−0.345170	−	0.832285i
$485$			20420.0i			1.91181i
$486$	−2388.10	+	2388.10i	−0.222894	+	0.222894i
$487$	−2051.96	−	2051.96i	−0.190930	−	0.190930i	0.605168	−	0.796098i	$-0.293106\pi$
$487$	−2051.96	−	2051.96i	−0.190930	−	0.190930i	−0.796098	+	0.605168i	$0.793106\pi$
$488$	−3387.59	+	3387.59i	−0.314239	+	0.314239i
$489$	−5428.87	+	5428.87i	−0.502049	+	0.502049i
$490$			2216.62i			0.204361i
$491$	−4611.78			−0.423883			−0.211942	−	0.977282i	$-0.567979\pi$
$491$	−4611.78			−0.423883			−0.211942	+	0.977282i	$0.567979\pi$
$492$	−5314.02	−	5314.02i	−0.486940	−	0.486940i
$493$			320.880i			0.0293138i
$494$	1565.01	+	950.821i	0.142537	+	0.0865981i
$495$	−5432.32	+	8133.89i	−0.493262	+	0.738568i
$496$	−2119.50	−	2119.50i	−0.191872	−	0.191872i
$497$			8052.42i			0.726762i
$498$		−	2439.32i		−	0.219495i
$499$	−8804.55	−	8804.55i	−0.789871	−	0.789871i	0.191601	−	0.981473i	$-0.438632\pi$
$499$	−8804.55	−	8804.55i	−0.789871	−	0.789871i	−0.981473	+	0.191601i	$0.938632\pi$
$500$	470.408	+	470.408i	0.0420746	+	0.0420746i
$501$	3421.87	+	3421.87i	0.305145	+	0.305145i
$502$	1463.28	+	1463.28i	0.130098	+	0.130098i
$503$			1508.07i			0.133681i	0.997764	+	0.0668404i	$0.0212918\pi$
$503$			1508.07i			0.133681i	−0.997764	+	0.0668404i	$0.978708\pi$
$504$			5066.52i			0.447780i
$505$	−3997.17	−	3997.17i	−0.352221	−	0.352221i
$506$	−164.922	+	246.940i	−0.0144895	+	0.0216953i
$507$	−3238.97	−	6238.35i	−0.283723	−	0.546459i
$508$			2976.64i			0.259974i
$509$	−2475.65	−	2475.65i	−0.215582	−	0.215582i	0.591052	−	0.806634i	$-0.298713\pi$
$509$	−2475.65	−	2475.65i	−0.215582	−	0.215582i	−0.806634	+	0.591052i	$0.798713\pi$
$510$	−1259.26			−0.109335
$511$			25010.1i			2.16513i
$512$	−8294.95	+	8294.95i	−0.715993	+	0.715993i
$513$	4346.88	−	4346.88i	0.374112	−	0.374112i
$514$	2878.36	+	2878.36i	0.247002	+	0.247002i
$515$	−8666.52	+	8666.52i	−0.741538	+	0.741538i
$516$			12007.2i			1.02440i
$517$	7527.83	+	5027.56i	0.640375	+	0.427682i
$518$	5479.89	−	5479.89i	0.464812	−	0.464812i
$519$	−2721.58			−0.230181
$520$	−8669.84	−	5267.36i	−0.731149	−	0.444209i
$521$	−17747.6			−1.49239			−0.746197	−	0.665725i	$-0.768122\pi$
$521$	−17747.6			−1.49239			−0.746197	+	0.665725i	$0.768122\pi$
$522$	−122.379	−	122.379i	−0.0102612	−	0.0102612i
$523$		−	785.436i		−	0.0656687i	−0.999461	−	0.0328343i	$-0.989547\pi$
$523$		−	785.436i		−	0.0656687i	0.999461	−	0.0328343i	$-0.0104534\pi$
$524$	−5044.60			−0.420562
$525$	−6607.08	+	6607.08i	−0.549250	+	0.549250i
$526$	1555.32	+	1555.32i	0.128926	+	0.128926i
$527$	−1284.86	−	1284.86i	−0.106204	−	0.106204i
$528$	−1040.06	−	5222.74i	−0.0857247	−	0.430475i
$529$	12083.3			0.993123
$530$	4082.87			0.334620
$531$	−9470.56	+	9470.56i	−0.773987	+	0.773987i
$532$		−	7067.72i		−	0.575986i
$533$	−3622.50	−	14838.5i	−0.294387	−	1.20586i
$534$			242.542i			0.0196551i
$535$	9179.15	−	9179.15i	0.741774	−	0.741774i
$536$		−	4604.93i		−	0.371087i
$537$		−	7888.11i		−	0.633886i
$538$	−2697.83	+	2697.83i	−0.216193	+	0.216193i
$539$	−5573.10	+	1109.83i	−0.445363	+	0.0886894i
$540$	−11413.5	+	11413.5i	−0.909555	+	0.909555i
$541$	4036.26	+	4036.26i	0.320762	+	0.320762i	0.849059	−	0.528297i	$-0.177169\pi$
$541$	4036.26	+	4036.26i	0.320762	+	0.320762i	−0.528297	+	0.849059i	$0.677169\pi$
$542$	−5522.27			−0.437642
$543$			4986.67i			0.394104i
$544$	−2911.21	+	2911.21i	−0.229444	+	0.229444i
$545$	22609.7			1.77705
$546$	1547.40	−	2546.96i	0.121287	−	0.199633i
$547$			955.912i			0.0747200i	0.999302	+	0.0373600i	$0.0118948\pi$
$547$			955.912i			0.0747200i	−0.999302	+	0.0373600i	$0.988105\pi$
$548$	−9456.45	−	9456.45i	−0.737152	−	0.737152i
$549$			5934.56i			0.461350i
$550$	2357.82	−	3530.39i	0.182796	−	0.273703i
$551$	360.186	+	360.186i	0.0278483	+	0.0278483i
$552$	−280.042	+	280.042i	−0.0215931	+	0.0215931i
$553$	9412.45	−	9412.45i	0.723794	−	0.723794i
$554$	−2698.01	+	2698.01i	−0.206909	+	0.206909i
$555$	19953.6			1.52610
$556$	−1463.05			−0.111596
$557$	−6138.96	−	6138.96i	−0.466995	−	0.466995i	0.433945	−	0.900940i	$-0.357121\pi$
$557$	−6138.96	−	6138.96i	−0.466995	−	0.466995i	−0.900940	+	0.433945i	$0.857121\pi$
$558$	980.053			0.0743530
$559$	−12671.4	+	20856.6i	−0.958754	+	1.57807i
$560$			16295.1i			1.22963i
$561$	−630.491	−	3166.08i	−0.0474499	−	0.238274i
$562$	−1739.11			−0.130534
$563$	−14136.6			−1.05823			−0.529117	−	0.848549i	$-0.677477\pi$
$563$	−14136.6			−1.05823			−0.529117	+	0.848549i	$0.677477\pi$
$564$	4046.22	+	4046.22i	0.302086	+	0.302086i
$565$	10902.1	+	10902.1i	0.811779	+	0.811779i
$566$	−3698.41	+	3698.41i	−0.274657	+	0.274657i
$567$	73.4523	+	73.4523i	0.00544040	+	0.00544040i
$568$		−	4879.46i		−	0.360454i
$569$	−18366.8			−1.35321			−0.676603	−	0.736348i	$-0.736549\pi$
$569$	−18366.8			−1.35321			−0.676603	+	0.736348i	$0.736549\pi$
$570$	−1413.52	+	1413.52i	−0.103870	+	0.103870i
$571$	23271.6			1.70558			0.852791	−	0.522253i	$-0.174908\pi$
$571$	23271.6			1.70558			0.852791	+	0.522253i	$0.174908\pi$
$572$	4219.50	−	11581.5i	0.308437	−	0.846586i
$573$	−2943.44			−0.214597
$574$	4579.18	−	4579.18i	0.332982	−	0.332982i
$575$	1196.16			0.0867538
$576$			3897.99i			0.281973i
$577$	−16404.7	−	16404.7i	−1.18360	−	1.18360i	−0.978804	−	0.204798i	$-0.934346\pi$
$577$	−16404.7	−	16404.7i	−1.18360	−	1.18360i	−0.204798	−	0.978804i	$-0.565654\pi$
$578$	2610.03	−	2610.03i	0.187825	−	0.187825i
$579$	−7669.08	−	7669.08i	−0.550459	−	0.550459i
$580$	−945.735	−	945.735i	−0.0677060	−	0.0677060i
$581$	−19135.2			−1.36637
$582$	3635.07			0.258897
$583$	2044.23	+	10265.3i	0.145220	+	0.729236i
$584$		−	15155.2i		−	1.07385i
$585$	−12208.0	+	2980.33i	−0.862800	+	0.210635i
$586$	−1974.83			−0.139214
$587$	6620.73	+	6620.73i	0.465531	+	0.465531i	0.900463	−	0.434932i	$-0.143228\pi$
$587$	6620.73	+	6620.73i	0.465531	+	0.465531i	−0.434932	+	0.900463i	$0.643228\pi$
$588$	−3592.09			−0.251930
$589$	−2884.50			−0.201789
$590$	8039.71	−	8039.71i	0.560999	−	0.560999i
$591$	−6196.66	+	6196.66i	−0.431297	+	0.431297i
$592$	12580.6	−	12580.6i	0.873408	−	0.873408i
$593$	−15795.0	−	15795.0i	−1.09380	−	1.09380i	−0.995119	−	0.0986824i	$-0.968537\pi$
$593$	−15795.0	−	15795.0i	−1.09380	−	1.09380i	−0.0986824	−	0.995119i	$-0.531463\pi$
$594$	3780.04	+	2524.54i	0.261106	+	0.174383i
$595$			9878.25i			0.680620i
$596$	10422.8	+	10422.8i	0.716332	+	0.716332i
$597$			10927.3i			0.749117i
$598$	−370.627	+	90.4810i	−0.0253446	+	0.00618736i
$599$	9729.13			0.663642			0.331821	−	0.943342i	$-0.392337\pi$
$599$	9729.13			0.663642			0.331821	+	0.943342i	$0.392337\pi$
$600$	4003.64	−	4003.64i	0.272413	−	0.272413i
$601$			1528.36i			0.103732i	0.998654	+	0.0518660i	$0.0165169\pi$
$601$			1528.36i			0.103732i	−0.998654	+	0.0518660i	$0.983483\pi$
$602$	−10346.8			−0.700507
$603$	−4033.59	−	4033.59i	−0.272405	−	0.272405i
$604$	−16280.7	+	16280.7i	−1.09677	+	1.09677i
$605$	19669.7	+	8137.38i	1.32180	+	0.546829i
$606$	−711.555	+	711.555i	−0.0476979	+	0.0476979i
$607$			20070.8i			1.34209i	0.741416	+	0.671046i	$0.234155\pi$
$607$			20070.8i			1.34209i	−0.741416	+	0.671046i	$0.765845\pi$
$608$			6535.65i			0.435947i
$609$	586.181	−	586.181i	0.0390037	−	0.0390037i
$610$		−	5037.95i		−	0.334394i
$611$	2758.26	+	11298.4i	0.182631	+	0.748089i
$612$			3342.02i			0.220740i
$613$	−11836.4	+	11836.4i	−0.779882	+	0.779882i	−0.979810	−	0.199929i	$-0.935929\pi$
$613$	−11836.4	+	11836.4i	−0.779882	+	0.779882i	0.199929	+	0.979810i	$0.435929\pi$
$614$	−4288.35			−0.281862
$615$	16673.9			1.09326
$616$	10813.8	−	2153.47i	0.707309	−	0.140853i
$617$	−12119.0	−	12119.0i	−0.790747	−	0.790747i	0.190868	−	0.981616i	$-0.438870\pi$
$617$	−12119.0	−	12119.0i	−0.790747	−	0.790747i	−0.981616	+	0.190868i	$0.938870\pi$
$618$	1542.77	+	1542.77i	0.100419	+	0.100419i
$619$	1357.31	−	1357.31i	0.0881338	−	0.0881338i	−0.661665	−	0.749799i	$-0.730150\pi$
$619$	1357.31	−	1357.31i	0.0881338	−	0.0881338i	0.749799	+	0.661665i	$0.230150\pi$
$620$	7573.79			0.490598
$621$			1280.75i			0.0827610i
$622$	−4820.37	−	4820.37i	−0.310739	−	0.310739i
$623$	1902.62			0.122354
$624$	3552.48	−	5847.22i	0.227905	−	0.375122i
$625$	14870.3			0.951702
$626$	−3260.94	+	3260.94i	−0.208200	+	0.208200i
$627$	−4261.63	−	2846.18i	−0.271440	−	0.181285i
$628$			15718.5i			0.998784i
$629$	7626.45	−	7626.45i	0.483444	−	0.483444i
$630$	−3767.41	−	3767.41i	−0.238250	−	0.238250i
$631$	12124.8	−	12124.8i	0.764946	−	0.764946i	−0.212266	−	0.977212i	$-0.568084\pi$
$631$	12124.8	−	12124.8i	0.764946	−	0.764946i	0.977212	+	0.212266i	$0.0680843\pi$
$632$	−5703.59	+	5703.59i	−0.358982	+	0.358982i
$633$			9683.66i			0.608043i
$634$	−6066.56			−0.380022
$635$	−4669.94	−	4669.94i	−0.291844	−	0.291844i
$636$			6616.38i			0.412511i
$637$	−6239.47	−	3790.79i	−0.388096	−	0.235787i
$638$	−209.186	+	313.217i	−0.0129808	+	0.0194363i
$639$	−4274.06	−	4274.06i	−0.264600	−	0.264600i
$640$		−	22354.7i		−	1.38070i
$641$			3688.64i			0.227289i	0.993521	+	0.113645i	$0.0362526\pi$
$641$			3688.64i			0.227289i	−0.993521	+	0.113645i	$0.963747\pi$
$642$	−1634.02	−	1634.02i	−0.100451	−	0.100451i
$643$	10767.6	+	10767.6i	0.660391	+	0.660391i	0.955472	−	0.295081i	$-0.0953467\pi$
$643$	10767.6	+	10767.6i	0.660391	+	0.660391i	−0.295081	+	0.955472i	$0.595347\pi$
$644$	1041.20	+	1041.20i	0.0637098	+	0.0637098i
$645$	−18837.7	−	18837.7i	−1.14997	−	1.14997i
$646$			1080.52i			0.0658086i
$647$		−	18357.1i		−	1.11545i	−0.830027	−	0.557723i	$-0.811675\pi$
$647$		−	18357.1i		−	1.11545i	0.830027	−	0.557723i	$-0.188325\pi$
$648$	−44.5093	−	44.5093i	−0.00269829	−	0.00269829i
$649$	24239.0	+	16188.3i	1.46605	+	0.979118i
$650$	5298.69	−	1293.57i	0.319741	−	0.0780583i
$651$			4694.35i			0.282621i
$652$	−12231.1	−	12231.1i	−0.734675	−	0.734675i
$653$	1133.58			0.0679330			0.0339665	−	0.999423i	$-0.489186\pi$
$653$	1133.58			0.0679330			0.0339665	+	0.999423i	$0.489186\pi$
$654$		−	4024.85i		−	0.240649i
$655$	7914.28	−	7914.28i	0.472117	−	0.472117i
$656$	10512.7	−	10512.7i	0.625691	−	0.625691i
$657$	−13274.8	−	13274.8i	−0.788281	−	0.788281i
$658$	−3486.70	+	3486.70i	−0.206574	+	0.206574i
$659$		−	10971.8i		−	0.648559i	−0.945961	−	0.324279i	$-0.894878\pi$
$659$		−	10971.8i		−	0.648559i	0.945961	−	0.324279i	$-0.105122\pi$
$660$	11189.7	+	7473.17i	0.659936	+	0.440747i
$661$	4551.90	−	4551.90i	0.267849	−	0.267849i	−0.560384	−	0.828233i	$-0.689346\pi$
$661$	4551.90	−	4551.90i	0.267849	−	0.267849i	0.828233	+	0.560384i	$0.189346\pi$
$662$	−1597.26			−0.0937754
$663$	2153.54	−	3544.64i	0.126149	−	0.207636i
$664$	11595.2			0.677681
$665$	11088.3	+	11088.3i	0.646595	+	0.646595i
$666$			5817.22i			0.338458i
$667$	−106.124			−0.00616061
$668$	−7709.40	+	7709.40i	−0.446535	+	0.446535i
$669$	−5943.31	−	5943.31i	−0.343471	−	0.343471i
$670$	3424.18	+	3424.18i	0.197444	+	0.197444i
$671$	12666.6	−	2522.42i	0.728744	−	0.145122i
$672$	10636.4			0.610576
$673$	5741.98			0.328881			0.164440	−	0.986387i	$-0.447418\pi$
$673$	5741.98			0.328881			0.164440	+	0.986387i	$0.447418\pi$
$674$	4557.20	−	4557.20i	0.260440	−	0.260440i
$675$		−	18310.3i		−	1.04409i
$676$	14054.9	−	7297.34i	0.799663	−	0.415188i
$677$			6643.49i			0.377149i	0.982059	+	0.188575i	$0.0603868\pi$
$677$			6643.49i			0.377149i	−0.982059	+	0.188575i	$0.939613\pi$
$678$	1940.74	−	1940.74i	0.109931	−	0.109931i
$679$		−	28515.2i		−	1.61165i
$680$		−	5985.84i		−	0.337568i
$681$	12781.7	−	12781.7i	0.719231	−	0.719231i
$682$	−416.560	−	2091.80i	−0.0233884	−	0.117447i
$683$	−24204.3	+	24204.3i	−1.35600	+	1.35600i	−0.477220	+	0.878784i	$0.658355\pi$
$683$	−24204.3	+	24204.3i	−1.35600	+	1.35600i	−0.878784	+	0.477220i	$0.841645\pi$
$684$	3751.40	+	3751.40i	0.209705	+	0.209705i
$685$	29671.7			1.65503
$686$			3721.00i			0.207097i
$687$	4498.26	−	4498.26i	0.249810	−	0.249810i
$688$	−23753.9			−1.31629
$689$	−6982.38	+	11492.7i	−0.386078	+	0.635467i
$690$		−	416.473i		−	0.0229780i
$691$	6938.93	+	6938.93i	0.382010	+	0.382010i	0.871826	−	0.489816i	$-0.162936\pi$
$691$	6938.93	+	6938.93i	0.382010	+	0.382010i	−0.489816	+	0.871826i	$0.662936\pi$
$692$		−	6131.67i		−	0.336837i
$693$	7585.87	−	11358.4i	0.415820	−	0.622613i
$694$	3743.32	+	3743.32i	0.204747	+	0.204747i
$695$	2295.33	−	2295.33i	0.125276	−	0.125276i
$696$	−355.203	+	355.203i	−0.0193447	+	0.0193447i
$697$	6372.92	−	6372.92i	0.346329	−	0.346329i
$698$	6231.81			0.337933
$699$	−19504.2			−1.05539
$700$	−14885.6	−	14885.6i	−0.803748	−	0.803748i
$701$	−864.409			−0.0465738			−0.0232869	−	0.999729i	$-0.507413\pi$
$701$	−864.409			−0.0465738			−0.0232869	+	0.999729i	$0.507413\pi$
$702$	1385.04	+	5673.37i	0.0744657	+	0.305025i
$703$		−	17121.3i		−	0.918552i
$704$	8319.77	−	1656.80i	0.445402	−	0.0886972i
$705$	−12695.9			−0.678236
$706$	1361.23			0.0725648
$707$	5581.78	+	5581.78i	0.296923	+	0.296923i
$708$	13028.5	+	13028.5i	0.691584	+	0.691584i
$709$	−4112.50	+	4112.50i	−0.217840	+	0.217840i	−0.807587	−	0.589748i	$-0.799227\pi$
$709$	−4112.50	+	4112.50i	−0.217840	+	0.217840i	0.589748	+	0.807587i	$0.299227\pi$
$710$	3628.32	+	3628.32i	0.191786	+	0.191786i
$711$			9991.87i			0.527038i
$712$	−1152.91			−0.0606843
$713$	424.939	−	424.939i	0.0223199	−	0.0223199i
$714$	1758.47			0.0921698
$715$	11550.0	+	24789.6i	0.604119	+	1.29661i
$716$	17771.8			0.927600
$717$	−15168.6	+	15168.6i	−0.790071	+	0.790071i
$718$	−6466.84			−0.336129
$719$		−	14133.1i		−	0.733067i	−0.930405	−	0.366534i	$-0.880544\pi$
$719$		−	14133.1i		−	0.733067i	0.930405	−	0.366534i	$-0.119456\pi$
$720$	−8649.10	−	8649.10i	−0.447685	−	0.447685i
$721$	12102.2	−	12102.2i	0.625117	−	0.625117i
$722$	−3102.90	−	3102.90i	−0.159942	−	0.159942i
$723$	−4812.90	−	4812.90i	−0.247571	−	0.247571i
$724$	−11234.9			−0.576714
$725$	1517.20			0.0777208
$726$	1448.57	−	3501.49i	0.0740518	−	0.178998i
$727$		−	28366.2i		−	1.44710i	−0.690270	−	0.723552i	$-0.742508\pi$
$727$		−	28366.2i		−	1.44710i	0.690270	−	0.723552i	$-0.257492\pi$
$728$	12106.8	+	7355.51i	0.616359	+	0.374469i
$729$	12017.3			0.610542
$730$	11269.2	+	11269.2i	0.571360	+	0.571360i
$731$	−14399.8			−0.728587
$732$	8164.10			0.412232
$733$	−9874.55	+	9874.55i	−0.497578	+	0.497578i	−0.910683	−	0.413105i	$-0.864444\pi$
$733$	−9874.55	+	9874.55i	−0.497578	+	0.497578i	0.413105	+	0.910683i	$0.364444\pi$
$734$	1276.26	−	1276.26i	0.0641792	−	0.0641792i
$735$	5635.49	−	5635.49i	0.282814	−	0.282814i
$736$	−962.819	−	962.819i	−0.0482201	−	0.0482201i
$737$	−6894.75	+	10323.6i	−0.344602	+	0.515977i
$738$			4861.07i			0.242464i
$739$	5014.79	+	5014.79i	0.249624	+	0.249624i	0.820816	−	0.571192i	$-0.193519\pi$
$739$	5014.79	+	5014.79i	0.249624	+	0.249624i	−0.571192	+	0.820816i	$0.693519\pi$
$740$			44955.1i			2.23322i
$741$	−1561.50	−	6396.18i	−0.0774130	−	0.317098i
$742$	−5701.46			−0.282085
$743$	2883.05	−	2883.05i	0.142354	−	0.142354i	−0.632338	−	0.774692i	$-0.717905\pi$
$743$	2883.05	−	2883.05i	0.142354	−	0.142354i	0.774692	+	0.632338i	$0.217905\pi$
$744$		−	2844.60i		−	0.140172i
$745$	−32703.8			−1.60829
$746$	4554.75	+	4554.75i	0.223540	+	0.223540i
$747$	10156.5	−	10156.5i	0.497468	−	0.497468i
$748$	7133.11	−	1420.49i	0.348679	−	0.0694359i
$749$	−12818.1	+	12818.1i	−0.625316	+	0.625316i
$750$			262.752i			0.0127925i
$751$			33750.2i			1.63990i	0.572437	+	0.819949i	$0.305998\pi$
$751$			33750.2i			1.63990i	−0.572437	+	0.819949i	$0.694002\pi$
$752$	−8004.66	+	8004.66i	−0.388165	+	0.388165i
$753$		−	7440.39i		−	0.360084i
$754$	−470.101	+	114.765i	−0.0227056	+	0.00554312i
$755$		−	51084.3i		−	2.46245i
$756$	15938.2	−	15938.2i	0.766756	−	0.766756i
$757$	30198.1			1.44989			0.724946	−	0.688805i	$-0.241865\pi$
$757$	30198.1			1.44989			0.724946	+	0.688805i	$0.241865\pi$
$758$	−6870.18			−0.329203
$759$	1047.11	−	208.521i	0.0500759	−	0.00997210i
$760$	−6719.08	−	6719.08i	−0.320693	−	0.320693i
$761$	23965.9	+	23965.9i	1.14161	+	1.14161i	0.988156	+	0.153450i	$0.0490384\pi$
$761$	23965.9	+	23965.9i	1.14161	+	1.14161i	0.153450	+	0.988156i	$0.450962\pi$
$762$	−831.318	+	831.318i	−0.0395216	+	0.0395216i
$763$	−31572.9			−1.49805
$764$		−	6631.51i		−	0.314031i
$765$	−5243.17	−	5243.17i	−0.247800	−	0.247800i
$766$	−5007.63			−0.236205
$767$	8881.39	+	36379.8i	0.418108	+	1.71265i
$768$	1972.02			0.0926549
$769$	10896.3	−	10896.3i	0.510963	−	0.510963i	−0.403858	−	0.914822i	$-0.632331\pi$
$769$	10896.3	−	10896.3i	0.510963	−	0.510963i	0.914822	+	0.403858i	$0.132331\pi$
$770$	−6439.77	+	9642.35i	−0.301394	+	0.451281i
$771$		−	14635.8i		−	0.683650i
$772$	17278.3	−	17278.3i	0.805517	−	0.805517i
$773$	−28124.4	−	28124.4i	−1.30862	−	1.30862i	−0.922412	−	0.386207i	$-0.873785\pi$
$773$	−28124.4	−	28124.4i	−1.30862	−	1.30862i	−0.386207	−	0.922412i	$-0.626215\pi$
$774$	5491.88	−	5491.88i	0.255041	−	0.255041i
$775$	−6075.17	+	6075.17i	−0.281582	+	0.281582i
$776$			17279.1i			0.799335i
$777$	−27863.9			−1.28650
$778$	−4695.16	−	4695.16i	−0.216362	−	0.216362i
$779$		−	14307.1i		−	0.658032i
$780$	4100.00	+	16794.4i	0.188210	+	0.770942i
$781$	−7305.79	+	10939.1i	−0.334727	+	0.501191i
$782$	−159.179	−	159.179i	−0.00727909	−	0.00727909i
$783$			1624.49i			0.0741437i
$784$		−	7106.23i		−	0.323717i
$785$	−24660.2	−	24660.2i	−1.12122	−	1.12122i
$786$	−1408.86	−	1408.86i	−0.0639343	−	0.0639343i
$787$	19810.6	+	19810.6i	0.897297	+	0.897297i	0.995196	−	0.0978994i	$-0.0312123\pi$
$787$	19810.6	+	19810.6i	0.897297	+	0.897297i	−0.0978994	+	0.995196i	$0.531212\pi$
$788$	−13961.0	−	13961.0i	−0.631141	−	0.631141i
$789$		−	7908.39i		−	0.356839i
$790$		−	8482.26i		−	0.382007i
$791$	−15224.1	−	15224.1i	−0.684330	−	0.684330i
$792$	−4596.75	+	6882.77i	−0.206235	+	0.308799i
$793$	14181.1	+	8615.71i	0.635038	+	0.385817i
$794$		−	3923.78i		−	0.175378i
$795$	−10380.2	−	10380.2i	−0.463079	−	0.463079i
$796$	−24618.9			−1.09622
$797$			25101.5i			1.11561i	0.829972	+	0.557806i	$0.188357\pi$
$797$			25101.5i			1.11561i	−0.829972	+	0.557806i	$0.811643\pi$
$798$	1973.88	−	1973.88i	0.0875621	−	0.0875621i
$799$	−4852.50	+	4852.50i	−0.214855	+	0.214855i
$800$	13765.0	+	13765.0i	0.608332	+	0.608332i
$801$	−1009.87	+	1009.87i	−0.0445467	+	0.0445467i
$802$		−	8373.99i		−	0.368698i
$803$	−22691.1	+	33975.8i	−0.997201	+	1.49312i
$804$	−5548.96	+	5548.96i	−0.243404	+	0.243404i
$805$	−3267.01			−0.143040
$806$	1422.83	−	2341.91i	0.0621798	−	0.102345i
$807$	13717.8			0.598375
$808$	−3382.34	−	3382.34i	−0.147265	−	0.147265i
$809$		−	17175.2i		−	0.746413i	−0.927748	−	0.373206i	$-0.878258\pi$
$809$		−	17175.2i		−	0.746413i	0.927748	−	0.373206i	$-0.121742\pi$
$810$	66.1933			0.00287135
$811$	11979.0	−	11979.0i	0.518669	−	0.518669i	−0.398500	−	0.917168i	$-0.630469\pi$
$811$	11979.0	−	11979.0i	0.518669	−	0.518669i	0.917168	+	0.398500i	$0.130469\pi$
$812$	1320.65	+	1320.65i	0.0570762	+	0.0570762i
$813$	14039.7	+	14039.7i	0.605649	+	0.605649i
$814$	12416.1	−	2472.54i	0.534625	−	0.106465i
$815$	38377.9			1.64947
$816$	4037.05			0.173192
$817$	−16163.7	+	16163.7i	−0.692164	+	0.692164i
$818$		−	103.410i		−	0.00442011i
$819$	17047.6	−	4161.83i	0.727340	−	0.177565i
$820$			37566.0i			1.59983i
$821$	−21097.8	+	21097.8i	−0.896857	+	0.896857i	−0.995157	−	0.0982996i	$-0.968660\pi$
$821$	−21097.8	+	21097.8i	−0.896857	+	0.896857i	0.0982996	+	0.995157i	$0.468660\pi$
$822$		−	5282.01i		−	0.224125i
$823$		−	16454.6i		−	0.696926i	−0.937323	−	0.348463i	$-0.886704\pi$
$823$		−	16454.6i		−	0.696926i	0.937323	−	0.348463i	$-0.113296\pi$
$824$	−7333.47	+	7333.47i	−0.310041	+	0.310041i
$825$	−14970.0	+	2981.13i	−0.631745	+	0.125806i
$826$	−11226.9	+	11226.9i	−0.472923	+	0.472923i
$827$	−1287.11	−	1287.11i	−0.0541198	−	0.0541198i	0.679529	−	0.733649i	$-0.262184\pi$
$827$	−1287.11	−	1287.11i	−0.0541198	−	0.0541198i	−0.733649	+	0.679529i	$0.762184\pi$
$828$	−1105.30			−0.0463910
$829$		−	12169.5i		−	0.509848i	−0.966961	−	0.254924i	$-0.917950\pi$
$829$		−	12169.5i		−	0.509848i	0.966961	−	0.254924i	$-0.0820504\pi$
$830$	−8622.06	+	8622.06i	−0.360573	+	0.360573i
$831$	13718.7			0.572680
$832$	9314.55	+	5659.05i	0.388130	+	0.235808i
$833$		−	4307.87i		−	0.179182i
$834$	−408.602	−	408.602i	−0.0169649	−	0.0169649i
$835$		−	24190.0i		−	1.00255i
$836$	6412.39	−	9601.37i	0.265284	−	0.397213i
$837$	−6504.75	−	6504.75i	−0.268623	−	0.268623i
$838$	−2764.63	+	2764.63i	−0.113965	+	0.113965i
$839$	29305.7	−	29305.7i	1.20589	−	1.20589i	0.233550	−	0.972345i	$-0.424966\pi$
$839$	29305.7	−	29305.7i	1.20589	−	1.20589i	0.972345	−	0.233550i	$-0.0750343\pi$
$840$	−10934.9	+	10934.9i	−0.449154	+	0.449154i
$841$	24254.4			0.994481
$842$	−14435.6			−0.590836
$843$	4421.48	+	4421.48i	0.180645	+	0.180645i
$844$	−21817.1			−0.889782
$845$	−10601.6	+	33498.7i	−0.431607	+	1.36377i
$846$		−	3701.34i		−	0.150419i
$847$	−27467.4	−	11363.3i	−1.11427	−	0.460977i
$848$	−13089.2			−0.530054
$849$	18805.5			0.760191
$850$	2275.72	+	2275.72i	0.0918312	+	0.0918312i
$851$	2522.28	+	2522.28i	0.101601	+	0.101601i
$852$	−5879.76	+	5879.76i	−0.236429	+	0.236429i
$853$	11902.9	+	11902.9i	0.477783	+	0.477783i	0.904422	−	0.426639i	$-0.140303\pi$
$853$	11902.9	+	11902.9i	0.477783	+	0.477783i	−0.426639	+	0.904422i	$0.640303\pi$
$854$			7035.15i			0.281895i
$855$	−11770.9			−0.470825
$856$	7767.25	−	7767.25i	0.310139	−	0.310139i
$857$	−27033.3			−1.07753			−0.538763	−	0.842457i	$-0.681108\pi$
$857$	−27033.3			−1.07753			−0.538763	+	0.842457i	$0.681108\pi$
$858$	4412.92	−	2056.07i	0.175588	−	0.0818100i
$859$	18383.2			0.730183			0.365092	−	0.930972i	$-0.381038\pi$
$859$	18383.2			0.730183			0.365092	+	0.930972i	$0.381038\pi$
$860$	42440.9	−	42440.9i	1.68282	−	1.68282i
$861$	−23284.0			−0.921622
$862$			709.569i			0.0280371i
$863$	−20450.9	−	20450.9i	−0.806669	−	0.806669i	0.177459	−	0.984128i	$-0.443212\pi$
$863$	−20450.9	−	20450.9i	−0.806669	−	0.806669i	−0.984128	+	0.177459i	$0.943212\pi$
$864$	−14738.3	+	14738.3i	−0.580334	+	0.580334i
$865$	9619.74	+	9619.74i	0.378128	+	0.378128i
$866$	2695.61	+	2695.61i	0.105774	+	0.105774i
$867$	−13271.3			−0.519860
$868$	−10576.3			−0.413574
$869$	21326.4	−	4246.92i	0.832505	−	0.165785i
$870$		−	528.251i		−	0.0205855i
$871$	−15494.5	+	3782.66i	−0.602767	+	0.147153i
$872$	19131.9			0.742993
$873$	15135.3	+	15135.3i	0.586771	+	0.586771i
$874$	−357.356			−0.0138304
$875$	2061.15			0.0796338
$876$	−18262.0	+	18262.0i	−0.704357	+	0.704357i
$877$	34452.9	−	34452.9i	1.32656	−	1.32656i	0.418207	−	0.908352i	$-0.362659\pi$
$877$	34452.9	−	34452.9i	1.32656	−	1.32656i	0.908352	−	0.418207i	$-0.137341\pi$
$878$	6340.20	−	6340.20i	0.243703	−	0.243703i
$879$	5020.75	+	5020.75i	0.192657	+	0.192657i
$880$	−14784.2	+	22136.6i	−0.566336	+	0.847983i
$881$			11853.0i			0.453279i	0.973979	+	0.226639i	$0.0727739\pi$
$881$			11853.0i			0.453279i	−0.973979	+	0.226639i	$0.927226\pi$
$882$	1642.95	+	1642.95i	0.0627224	+	0.0627224i
$883$		−	30926.0i		−	1.17865i	−0.807898	−	0.589323i	$-0.799395\pi$
$883$		−	30926.0i		−	1.17865i	0.807898	−	0.589323i	$-0.200605\pi$
$884$	7986.00	+	4851.89i	0.303844	+	0.184601i
$885$	−40879.9			−1.55273
$886$	4415.63	−	4415.63i	0.167433	−	0.167433i
$887$		−	18177.6i		−	0.688099i	−0.938952	−	0.344049i	$-0.888201\pi$
$887$		−	18177.6i		−	0.688099i	0.938952	−	0.344049i	$-0.111799\pi$
$888$	16884.4			0.638069
$889$	6521.25	+	6521.25i	0.246024	+	0.246024i
$890$	857.293	−	857.293i	0.0322882	−	0.0322882i
$891$	33.1419	+	166.425i	0.00124612	+	0.00625752i
$892$	13390.2	−	13390.2i	0.502619	−	0.502619i
$893$			10893.8i			0.408228i
$894$			5821.76i			0.217795i
$895$	−27881.4	+	27881.4i	−1.04131	+	1.04131i
$896$			31216.8i			1.16393i
$897$	1172.31	+	712.236i	0.0436369	+	0.0265116i
$898$			16435.6i			0.610760i
$899$	538.990	−	538.990i	0.0199959	−	0.0199959i
$900$	15801.9			0.585257
$901$	−7934.80			−0.293393
$902$	10375.3	−	2066.14i	0.382994	−	0.0762693i
$903$	26305.5	+	26305.5i	0.969427	+	0.969427i
$904$	9225.20	+	9225.20i	0.339409	+	0.339409i
$905$	17626.0	−	17626.0i	0.647412	−	0.647412i
$906$	−9093.76			−0.333466
$907$		−	470.180i		−	0.0172129i	−0.999963	−	0.00860643i	$-0.997260\pi$
$907$		−	470.180i		−	0.0172129i	0.999963	−	0.00860643i	$-0.00273955\pi$
$908$	28797.0	+	28797.0i	1.05249	+	1.05249i
$909$	−5925.38			−0.216207
$910$	−14472.0	+	3533.04i	−0.527189	+	0.128702i
$911$	−36408.0			−1.32410			−0.662048	−	0.749461i	$-0.730313\pi$
$911$	−36408.0			−1.32410			−0.662048	+	0.749461i	$0.730313\pi$
$912$	4531.57	−	4531.57i	0.164534	−	0.164534i
$913$	−25994.8	−	17360.9i	−0.942279	−	0.629313i
$914$			832.179i			0.0301160i
$915$	−12808.4	+	12808.4i	−0.462766	+	0.462766i
$916$	10134.5	+	10134.5i	0.365560	+	0.365560i
$917$	−11051.8	+	11051.8i	−0.397995	+	0.397995i
$918$	−2436.64	+	2436.64i	−0.0876047	+	0.0876047i
$919$		−	21025.3i		−	0.754690i	−0.926073	−	0.377345i	$-0.876837\pi$
$919$		−	21025.3i		−	0.754690i	0.926073	−	0.377345i	$-0.123163\pi$
$920$	1979.68			0.0709437
$921$	10902.6	+	10902.6i	0.390068	+	0.390068i
$922$			6778.68i			0.242130i
$923$	−16418.2	+	4008.17i	−0.585495	+	0.142937i
$924$	−15625.6	−	10435.8i	−0.556327	−	0.371550i
$925$	−36059.9	−	36059.9i	−1.28177	−	1.28177i
$926$			2998.96i			0.106427i
$927$			12847.2i			0.455186i
$928$	−1221.23	−	1221.23i	−0.0431993	−	0.0431993i
$929$	−24043.8	−	24043.8i	−0.849142	−	0.849142i	0.140884	−	0.990026i	$-0.455005\pi$
$929$	−24043.8	−	24043.8i	−0.849142	−	0.849142i	−0.990026	+	0.140884i	$0.955005\pi$
$930$	2115.21	+	2115.21i	0.0745813	+	0.0745813i
$931$	−4835.56	−	4835.56i	−0.170225	−	0.170225i
$932$		−	43942.6i		−	1.54441i
$933$			24510.4i			0.860059i
$934$	11787.4	+	11787.4i	0.412950	+	0.412950i
$935$	−8962.32	+	13419.4i	−0.313475	+	0.469371i
$936$	−10330.2	+	2521.91i	−0.360741	+	0.0880675i
$937$			51820.7i			1.80673i	0.428871	+	0.903366i	$0.358912\pi$
$937$			51820.7i			1.80673i	−0.428871	+	0.903366i	$0.641088\pi$
$938$	−4781.63	−	4781.63i	−0.166446	−	0.166446i
$939$	16581.1			0.576255
$940$		−	28603.7i		−	0.992500i
$941$	32378.9	−	32378.9i	1.12170	−	1.12170i	0.130216	−	0.991486i	$-0.458433\pi$
$941$	32378.9	−	32378.9i	1.12170	−	1.12170i	0.991486	−	0.130216i	$-0.0415669\pi$
$942$	−4389.87	+	4389.87i	−0.151836	+	0.151836i
$943$	2107.70	+	2107.70i	0.0727849	+	0.0727849i
$944$	−25774.4	+	25774.4i	−0.888649	+	0.888649i
$945$			50009.7i			1.72150i
$946$	−14056.0	−	9387.45i	−0.483085	−	0.322635i
$947$	27094.3	−	27094.3i	0.929722	−	0.929722i	−0.0679661	−	0.997688i	$-0.521651\pi$
$947$	27094.3	−	27094.3i	0.929722	−	0.929722i	0.997688	+	0.0679661i	$0.0216510\pi$
$948$	13745.7			0.470927
$949$	−50993.5	+	12449.0i	−1.74428	+	0.425829i
$950$	5108.97			0.174481
$951$	15423.5	+	15423.5i	0.525910	+	0.525910i
$952$			8358.82i			0.284570i
$953$	−11841.0			−0.402483			−0.201242	−	0.979542i	$-0.564498\pi$
$953$	−11841.0			−0.402483			−0.201242	+	0.979542i	$0.564498\pi$
$954$	3026.21	−	3026.21i	0.102702	−	0.102702i
$955$	10403.9	+	10403.9i	0.352527	+	0.352527i
$956$	−34174.5	−	34174.5i	−1.15615	−	1.15615i
$957$	1328.14	−	264.486i	0.0448619	−	0.00893378i
$958$	−14681.8			−0.495143
$959$	−41434.6			−1.39519
$960$	−8412.90	+	8412.90i	−0.282839	+	0.282839i
$961$		−	25474.6i		−	0.855110i
$962$	13900.7	+	8445.36i	0.465880	+	0.283045i
$963$		−	13607.1i		−	0.455330i
$964$	10843.4	−	10843.4i	0.362284	−	0.362284i
$965$			54214.5i			1.80853i
$966$			581.576i			0.0193705i
$967$	−5995.78	+	5995.78i	−0.199391	+	0.199391i	−0.799739	−	0.600348i	$-0.795029\pi$
$967$	−5995.78	+	5995.78i	−0.199391	+	0.199391i	0.600348	+	0.799739i	$0.295029\pi$
$968$	16644.2	+	6885.72i	0.552649	+	0.228632i
$969$	2747.08	−	2747.08i	0.0910721	−	0.0910721i
$970$	−12848.6	−	12848.6i	−0.425302	−	0.425302i
$971$	19184.1			0.634033			0.317017	−	0.948420i	$-0.397319\pi$
$971$	19184.1			0.634033			0.317017	+	0.948420i	$0.397319\pi$
$972$			27357.7i			0.902776i
$973$	−3205.27	+	3205.27i	−0.105608	+	0.105608i
$974$	2582.24			0.0849490
$975$	−16760.0	−	10182.5i	−0.550512	−	0.334463i
$976$			16151.1i			0.529696i
$977$	−28968.4	−	28968.4i	−0.948598	−	0.948598i	0.0501439	−	0.998742i	$-0.484032\pi$
$977$	−28968.4	−	28968.4i	−0.948598	−	0.948598i	−0.998742	+	0.0501439i	$0.984032\pi$
$978$		−	6831.84i		−	0.223372i
$979$	2584.67	+	1726.20i	0.0843782	+	0.0563530i
$980$	12696.6	+	12696.6i	0.413857	+	0.413857i
$981$	16758.2	−	16758.2i	0.545411	−	0.545411i
$982$	2901.80	−	2901.80i	0.0942974	−	0.0942974i
$983$	8281.02	−	8281.02i	0.268691	−	0.268691i	−0.559881	−	0.828573i	$-0.689153\pi$
$983$	8281.02	−	8281.02i	0.268691	−	0.268691i	0.828573	+	0.559881i	$0.189153\pi$
$984$	14109.2			0.457099
$985$	43805.7			1.41702
$986$	−201.902	−	201.902i	−0.00652117	−	0.00652117i
$987$	17729.0			0.571754
$988$	14410.5	−	3518.02i	0.464027	−	0.113283i
$989$		−	4762.42i		−	0.153121i
$990$	−1699.87	−	8536.05i	−0.0545710	−	0.274034i
$991$	−1249.67			−0.0400575			−0.0200287	−	0.999799i	$-0.506376\pi$
$991$	−1249.67			−0.0400575			−0.0200287	+	0.999799i	$0.506376\pi$
$992$	9780.08			0.313022
$993$	4060.84	+	4060.84i	0.129775	+	0.129775i
$994$	−5066.70	−	5066.70i	−0.161676	−	0.161676i
$995$	38623.7	−	38623.7i	1.23061	−	1.23061i
$996$	−13972.2	−	13972.2i	−0.444505	−	0.444505i
$997$		−	6377.58i		−	0.202588i	−0.994857	−	0.101294i	$-0.967702\pi$
$997$		−	6377.58i		−	0.202588i	0.994857	−	0.101294i	$-0.0322982\pi$
$998$	11079.9			0.351431
$999$	38609.7	−	38609.7i	1.22278	−	1.22278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.17	✓	80
11.10	odd	2	inner	143.4.g.a.21.24	yes	80
13.5	odd	4	inner	143.4.g.a.109.24	yes	80
143.109	even	4	inner	143.4.g.a.109.17	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.17	✓	80	1.1	even	1	trivial
143.4.g.a.21.24	yes	80	11.10	odd	2	inner
143.4.g.a.109.17	yes	80	143.109	even	4	inner
143.4.g.a.109.24	yes	80	13.5	odd	4	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.629214 + 0.629214i) q^{2} +3.19940 q^{3} +7.20818i q^{4} +(-11.3086 - 11.3086i) q^{5} +(-2.01311 + 2.01311i) q^{6} +(15.7918 + 15.7918i) q^{7} +(-9.56920 - 9.56920i) q^{8} -16.7639 q^{9} +O(q^{10})\)	\(q+(-0.629214 + 0.629214i) q^{2} +3.19940 q^{3} +7.20818i q^{4} +(-11.3086 - 11.3086i) q^{5} +(-2.01311 + 2.01311i) q^{6} +(15.7918 + 15.7918i) q^{7} +(-9.56920 - 9.56920i) q^{8} -16.7639 q^{9} +14.2311 q^{10} +(7.12528 + 35.7803i) q^{11} +23.0618i q^{12} +(-24.3375 + 40.0585i) q^{13} -19.8728 q^{14} +(-36.1808 - 36.1808i) q^{15} -45.6233 q^{16} -27.6573 q^{17} +(10.5481 - 10.5481i) q^{18} +(-31.0451 + 31.0451i) q^{19} +(81.5147 - 81.5147i) q^{20} +(50.5241 + 50.5241i) q^{21} +(-26.9968 - 18.0301i) q^{22} -9.14702i q^{23} +(-30.6157 - 30.6157i) q^{24} +130.771i q^{25} +(-9.89186 - 40.5189i) q^{26} -140.018 q^{27} +(-113.830 + 113.830i) q^{28} -11.6020i q^{29} +45.5310 q^{30} +(46.4566 + 46.4566i) q^{31} +(105.260 - 105.260i) q^{32} +(22.7966 + 114.475i) q^{33} +(17.4023 - 17.4023i) q^{34} -357.167i q^{35} -120.837i q^{36} +(-275.748 + 275.748i) q^{37} -39.0681i q^{38} +(-77.8654 + 128.163i) q^{39} +216.429i q^{40} +(-230.425 + 230.425i) q^{41} -63.5809 q^{42} +520.653 q^{43} +(-257.911 + 51.3603i) q^{44} +(189.577 + 189.577i) q^{45} +(5.75543 + 5.75543i) q^{46} +(175.451 - 175.451i) q^{47} -145.967 q^{48} +155.759i q^{49} +(-82.2828 - 82.2828i) q^{50} -88.4865 q^{51} +(-288.749 - 175.429i) q^{52} +286.898 q^{53} +(88.1013 - 88.1013i) q^{54} +(324.049 - 485.204i) q^{55} -302.229i q^{56} +(-99.3257 + 99.3257i) q^{57} +(7.30015 + 7.30015i) q^{58} +(564.939 - 564.939i) q^{59} +(260.798 - 260.798i) q^{60} -354.009i q^{61} -58.4623 q^{62} +(-264.731 - 264.731i) q^{63} -232.524i q^{64} +(728.232 - 177.783i) q^{65} +(-86.3735 - 57.6856i) q^{66} +(240.612 + 240.612i) q^{67} -199.358i q^{68} -29.2649i q^{69} +(224.734 + 224.734i) q^{70} +(254.957 + 254.957i) q^{71} +(160.417 + 160.417i) q^{72} +(791.873 + 791.873i) q^{73} -347.010i q^{74} +418.388i q^{75} +(-223.779 - 223.779i) q^{76} +(-452.513 + 677.554i) q^{77} +(-31.6480 - 129.636i) q^{78} -596.036i q^{79} +(515.937 + 515.937i) q^{80} +4.65131 q^{81} -289.973i q^{82} +(-605.860 + 605.860i) q^{83} +(-364.187 + 364.187i) q^{84} +(312.766 + 312.766i) q^{85} +(-327.602 + 327.602i) q^{86} -37.1194i q^{87} +(274.206 - 410.572i) q^{88} +(60.2408 - 60.2408i) q^{89} -238.568 q^{90} +(-1016.93 + 248.262i) q^{91} +65.9333 q^{92} +(148.633 + 148.633i) q^{93} +220.793i q^{94} +702.157 q^{95} +(336.770 - 336.770i) q^{96} +(-902.850 - 902.850i) q^{97} +(-98.0057 - 98.0057i) q^{98} +(-119.447 - 599.816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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