LMFDB - Embedded newform 143.4.g.a.21.9

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			21.9
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.51606 + 2.51606i) q^{2} -7.60421 q^{3} -4.66116i q^{4} +(2.32460 + 2.32460i) q^{5} +(19.1327 - 19.1327i) q^{6} +(-13.4109 - 13.4109i) q^{7} +(-8.40074 - 8.40074i) q^{8} +30.8240 q^{9} +O(q^{10})$	\(q+(-2.51606 + 2.51606i) q^{2} -7.60421 q^{3} -4.66116i q^{4} +(2.32460 + 2.32460i) q^{5} +(19.1327 - 19.1327i) q^{6} +(-13.4109 - 13.4109i) q^{7} +(-8.40074 - 8.40074i) q^{8} +30.8240 q^{9} -11.6977 q^{10} +(36.4774 - 0.633182i) q^{11} +35.4444i q^{12} +(-2.71648 - 46.7934i) q^{13} +67.4854 q^{14} +(-17.6768 - 17.6768i) q^{15} +79.5629 q^{16} -46.5700 q^{17} +(-77.5552 + 77.5552i) q^{18} +(-86.6577 + 86.6577i) q^{19} +(10.8353 - 10.8353i) q^{20} +(101.979 + 101.979i) q^{21} +(-90.1863 + 93.3726i) q^{22} +208.968i q^{23} +(63.8810 + 63.8810i) q^{24} -114.192i q^{25} +(124.570 + 110.900i) q^{26} -29.0785 q^{27} +(-62.5104 + 62.5104i) q^{28} -111.447i q^{29} +88.9518 q^{30} +(152.741 + 152.741i) q^{31} +(-132.979 + 132.979i) q^{32} +(-277.382 + 4.81485i) q^{33} +(117.173 - 117.173i) q^{34} -62.3501i q^{35} -143.676i q^{36} +(-271.761 + 271.761i) q^{37} -436.073i q^{38} +(20.6567 + 355.827i) q^{39} -39.0568i q^{40} +(186.564 - 186.564i) q^{41} -513.173 q^{42} +364.691 q^{43} +(-2.95136 - 170.027i) q^{44} +(71.6536 + 71.6536i) q^{45} +(-525.777 - 525.777i) q^{46} +(401.750 - 401.750i) q^{47} -605.013 q^{48} +16.7052i q^{49} +(287.316 + 287.316i) q^{50} +354.128 q^{51} +(-218.111 + 12.6620i) q^{52} +113.346 q^{53} +(73.1634 - 73.1634i) q^{54} +(86.2673 + 83.3235i) q^{55} +225.323i q^{56} +(658.964 - 658.964i) q^{57} +(280.407 + 280.407i) q^{58} +(174.977 - 174.977i) q^{59} +(-82.3943 + 82.3943i) q^{60} +680.960i q^{61} -768.610 q^{62} +(-413.378 - 413.378i) q^{63} -32.6665i q^{64} +(102.461 - 115.091i) q^{65} +(685.796 - 710.024i) q^{66} +(45.3079 + 45.3079i) q^{67} +217.070i q^{68} -1589.04i q^{69} +(156.877 + 156.877i) q^{70} +(389.508 + 389.508i) q^{71} +(-258.944 - 258.944i) q^{72} +(215.228 + 215.228i) q^{73} -1367.54i q^{74} +868.343i q^{75} +(403.926 + 403.926i) q^{76} +(-497.687 - 480.703i) q^{77} +(-947.256 - 843.309i) q^{78} +575.153i q^{79} +(184.952 + 184.952i) q^{80} -611.129 q^{81} +938.812i q^{82} +(276.317 - 276.317i) q^{83} +(475.342 - 475.342i) q^{84} +(-108.257 - 108.257i) q^{85} +(-917.587 + 917.587i) q^{86} +847.464i q^{87} +(-311.756 - 301.118i) q^{88} +(231.060 - 231.060i) q^{89} -360.570 q^{90} +(-591.112 + 663.973i) q^{91} +974.034 q^{92} +(-1161.47 - 1161.47i) q^{93} +2021.66i q^{94} -402.890 q^{95} +(1011.20 - 1011.20i) q^{96} +(-431.673 - 431.673i) q^{97} +(-42.0314 - 42.0314i) q^{98} +(1124.38 - 19.5172i) 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 $

$2$	−2.51606	+	2.51606i	−0.889563	+	0.889563i	−0.994481	−	0.104918i	$-0.966542\pi$
$2$	−2.51606	+	2.51606i	−0.889563	+	0.889563i	0.104918	+	0.994481i	$0.466542\pi$
$3$	−7.60421			−1.46343			−0.731715	−	0.681610i	$-0.761280\pi$
$3$	−7.60421			−1.46343			−0.731715	+	0.681610i	$0.761280\pi$
$4$		−	4.66116i		−	0.582645i
$5$	2.32460	+	2.32460i	0.207919	+	0.207919i	0.803382	−	0.595463i	$-0.203032\pi$
$5$	2.32460	+	2.32460i	0.207919	+	0.207919i	−0.595463	+	0.803382i	$0.703032\pi$
$6$	19.1327	−	19.1327i	1.30181	−	1.30181i
$7$	−13.4109	−	13.4109i	−0.724121	−	0.724121i	0.245321	−	0.969442i	$-0.421107\pi$
$7$	−13.4109	−	13.4109i	−0.724121	−	0.724121i	−0.969442	+	0.245321i	$0.921107\pi$
$8$	−8.40074	−	8.40074i	−0.371264	−	0.371264i
$9$	30.8240			1.14163
$10$	−11.6977			−0.369914
$11$	36.4774	−	0.633182i	0.999849	−	0.0173556i
$11$	36.4774	−	0.633182i	0.999849	−	0.0173556i
$12$			35.4444i			0.852661i
$13$	−2.71648	−	46.7934i	−0.0579552	−	0.998319i
$13$	−2.71648	−	46.7934i	−0.0579552	−	0.998319i
$14$	67.4854			1.28830
$15$	−17.6768	−	17.6768i	−0.304275	−	0.304275i
$16$	79.5629			1.24317
$17$	−46.5700			−0.664405			−0.332203	−	0.943208i	$-0.607792\pi$
$17$	−46.5700			−0.664405			−0.332203	+	0.943208i	$0.607792\pi$
$18$	−77.5552	+	77.5552i	−1.01555	+	1.01555i
$19$	−86.6577	+	86.6577i	−1.04635	+	1.04635i	−0.0474777	+	0.998872i	$0.515118\pi$
$19$	−86.6577	+	86.6577i	−1.04635	+	1.04635i	−0.998872	+	0.0474777i	$0.984882\pi$
$20$	10.8353	−	10.8353i	0.121143	−	0.121143i
$21$	101.979	+	101.979i	1.05970	+	1.05970i
$22$	−90.1863	+	93.3726i	−0.873990	+	0.904868i
$23$			208.968i			1.89447i	0.320535	+	0.947237i	$0.396137\pi$
$23$			208.968i			1.89447i	−0.320535	+	0.947237i	$0.603863\pi$
$24$	63.8810	+	63.8810i	0.543319	+	0.543319i
$25$		−	114.192i		−	0.913539i
$26$	124.570	+	110.900i	0.939623	+	0.836513i
$27$	−29.0785			−0.207265
$28$	−62.5104	+	62.5104i	−0.421906	+	0.421906i
$29$		−	111.447i		−	0.713626i	−0.934176	−	0.356813i	$-0.883863\pi$
$29$		−	111.447i		−	0.713626i	0.934176	−	0.356813i	$-0.116137\pi$
$30$	88.9518			0.541343
$31$	152.741	+	152.741i	0.884936	+	0.884936i	0.994031	−	0.109096i	$-0.0347955\pi$
$31$	152.741	+	152.741i	0.884936	+	0.884936i	−0.109096	+	0.994031i	$0.534795\pi$
$32$	−132.979	+	132.979i	−0.734614	+	0.734614i
$33$	−277.382	+	4.81485i	−1.46321	+	0.0253987i
$34$	117.173	−	117.173i	0.591030	−	0.591030i
$35$		−	62.3501i		−	0.301117i
$36$		−	143.676i		−	0.665165i
$37$	−271.761	+	271.761i	−1.20749	+	1.20749i	−0.235658	+	0.971836i	$0.575725\pi$
$37$	−271.761	+	271.761i	−1.20749	+	1.20749i	−0.971836	+	0.235658i	$0.924275\pi$
$38$		−	436.073i		−	1.86159i
$39$	20.6567	+	355.827i	0.0848134	+	1.46097i
$40$		−	39.0568i		−	0.154385i
$41$	186.564	−	186.564i	0.710642	−	0.710642i	−0.256027	−	0.966670i	$-0.582414\pi$
$41$	186.564	−	186.564i	0.710642	−	0.710642i	0.966670	+	0.256027i	$0.0824137\pi$
$42$	−513.173			−1.88534
$43$	364.691			1.29337			0.646685	−	0.762757i	$-0.276155\pi$
$43$	364.691			1.29337			0.646685	+	0.762757i	$0.276155\pi$
$44$	−2.95136	−	170.027i	−0.0101122	−	0.582557i
$45$	71.6536	+	71.6536i	0.237366	+	0.237366i
$46$	−525.777	−	525.777i	−1.68525	−	1.68525i
$47$	401.750	−	401.750i	1.24683	−	1.24683i	0.289725	−	0.957110i	$-0.406436\pi$
$47$	401.750	−	401.750i	1.24683	−	1.24683i	0.957110	−	0.289725i	$-0.0935638\pi$
$48$	−605.013			−1.81929
$49$			16.7052i			0.0487033i
$50$	287.316	+	287.316i	0.812651	+	0.812651i
$51$	354.128			0.972311
$52$	−218.111	+	12.6620i	−0.581666	+	0.0337673i
$53$	113.346			0.293760			0.146880	−	0.989154i	$-0.453077\pi$
$53$	113.346			0.293760			0.146880	+	0.989154i	$0.453077\pi$
$54$	73.1634	−	73.1634i	0.184375	−	0.184375i
$55$	86.2673	+	83.3235i	0.211496	+	0.204279i
$56$			225.323i			0.537680i
$57$	658.964	−	658.964i	1.53126	−	1.53126i
$58$	280.407	+	280.407i	0.634815	+	0.634815i
$59$	174.977	−	174.977i	0.386103	−	0.386103i	−0.487192	−	0.873295i	$-0.661979\pi$
$59$	174.977	−	174.977i	0.386103	−	0.386103i	0.873295	+	0.487192i	$0.161979\pi$
$60$	−82.3943	+	82.3943i	−0.177284	+	0.177284i
$61$			680.960i			1.42931i	0.699476	+	0.714656i	$0.253417\pi$
$61$			680.960i			1.42931i	−0.699476	+	0.714656i	$0.746583\pi$
$62$	−768.610			−1.57441
$63$	−413.378	−	413.378i	−0.826678	−	0.826678i
$64$		−	32.6665i		−	0.0638018i
$65$	102.461	−	115.091i	0.195519	−	0.219619i
$66$	685.796	−	710.024i	1.27902	−	1.32421i
$67$	45.3079	+	45.3079i	0.0826154	+	0.0826154i	0.747207	−	0.664591i	$-0.231394\pi$
$67$	45.3079	+	45.3079i	0.0826154	+	0.0826154i	−0.664591	+	0.747207i	$0.731394\pi$
$68$			217.070i			0.387112i
$69$		−	1589.04i		−	2.77243i
$70$	156.877	+	156.877i	0.267863	+	0.267863i
$71$	389.508	+	389.508i	0.651071	+	0.651071i	0.953251	−	0.302180i	$-0.0977143\pi$
$71$	389.508	+	389.508i	0.651071	+	0.651071i	−0.302180	+	0.953251i	$0.597714\pi$
$72$	−258.944	−	258.944i	−0.423846	−	0.423846i
$73$	215.228	+	215.228i	0.345076	+	0.345076i	0.858272	−	0.513196i	$-0.171538\pi$
$73$	215.228	+	215.228i	0.345076	+	0.345076i	−0.513196	+	0.858272i	$0.671538\pi$
$74$		−	1367.54i		−	2.14828i
$75$			868.343i			1.33690i
$76$	403.926	+	403.926i	0.609651	+	0.609651i
$77$	−497.687	−	480.703i	−0.736580	−	0.711445i
$78$	−947.256	−	843.309i	−1.37507	−	1.22418i
$79$			575.153i			0.819111i	0.912285	+	0.409556i	$0.134316\pi$
$79$			575.153i			0.819111i	−0.912285	+	0.409556i	$0.865684\pi$
$80$	184.952	+	184.952i	0.258478	+	0.258478i
$81$	−611.129			−0.838311
$82$			938.812i			1.26432i
$83$	276.317	−	276.317i	0.365418	−	0.365418i	−0.500385	−	0.865803i	$-0.666808\pi$
$83$	276.317	−	276.317i	0.365418	−	0.365418i	0.865803	+	0.500385i	$0.166808\pi$
$84$	475.342	−	475.342i	0.617430	−	0.617430i
$85$	−108.257	−	108.257i	−0.138142	−	0.138142i
$86$	−917.587	+	917.587i	−1.15053	+	1.15053i
$87$			847.464i			1.04434i
$88$	−311.756	−	301.118i	−0.377651	−	0.364764i
$89$	231.060	−	231.060i	0.275195	−	0.275195i	−0.555993	−	0.831187i	$-0.687662\pi$
$89$	231.060	−	231.060i	0.275195	−	0.275195i	0.831187	+	0.555993i	$0.187662\pi$
$90$	−360.570			−0.422305
$91$	−591.112	+	663.973i	−0.680938	+	0.764871i
$92$	974.034			1.10381
$93$	−1161.47	−	1161.47i	−1.29504	−	1.29504i
$94$			2021.66i			2.21828i
$95$	−402.890			−0.435112
$96$	1011.20	−	1011.20i	1.07506	−	1.07506i
$97$	−431.673	−	431.673i	−0.451853	−	0.451853i	0.444116	−	0.895969i	$-0.353518\pi$
$97$	−431.673	−	431.673i	−0.451853	−	0.451853i	−0.895969	+	0.444116i	$0.853518\pi$
$98$	−42.0314	−	42.0314i	−0.0433246	−	0.0433246i
$99$	1124.38	−	19.5172i	1.14146	−	0.0198137i
$100$	−532.269			−0.532269
$101$	1675.75			1.65092			0.825462	−	0.564458i	$-0.190915\pi$
$101$	1675.75			1.65092			0.825462	+	0.564458i	$0.190915\pi$
$102$	−891.009	+	891.009i	−0.864932	+	0.864932i
$103$		−	217.688i		−	0.208247i	−0.994564	−	0.104123i	$-0.966796\pi$
$103$		−	217.688i		−	0.208247i	0.994564	−	0.104123i	$-0.0332037\pi$
$104$	−370.278	+	415.919i	−0.349123	+	0.392156i
$105$			474.123i			0.440664i
$106$	−285.186	+	285.186i	−0.261318	+	0.261318i
$107$			758.902i			0.685662i	0.939397	+	0.342831i	$0.111386\pi$
$107$			758.902i			0.685662i	−0.939397	+	0.342831i	$0.888614\pi$
$108$			135.540i			0.120762i
$109$	93.5650	−	93.5650i	0.0822193	−	0.0822193i	−0.664801	−	0.747020i	$-0.731484\pi$
$109$	93.5650	−	93.5650i	0.0822193	−	0.0822193i	0.747020	+	0.664801i	$0.231484\pi$
$110$	−426.702	+	7.40678i	−0.369858	+	0.00642008i
$111$	2066.53	−	2066.53i	1.76708	−	1.76708i
$112$	−1067.01	−	1067.01i	−0.900206	−	0.900206i
$113$	1005.85			0.837366			0.418683	−	0.908132i	$-0.362492\pi$
$113$	1005.85			0.837366			0.418683	+	0.908132i	$0.362492\pi$
$114$			3315.99i			2.72431i
$115$	−485.768	+	485.768i	−0.393897	+	0.393897i
$116$	−519.471			−0.415790
$117$	−83.7329	−	1442.36i	−0.0661633	−	1.13971i
$118$			880.508i			0.686927i
$119$	624.546	+	624.546i	0.481110	+	0.481110i
$120$			296.996i			0.225932i
$121$	1330.20	−	46.1937i	0.999398	−	0.0347060i
$122$	−1713.34	−	1713.34i	−1.27146	−	1.27146i
$123$	−1418.67	+	1418.67i	−1.03998	+	1.03998i
$124$	711.948	−	711.948i	0.515603	−	0.515603i
$125$	556.028	−	556.028i	0.397861	−	0.397861i
$126$	2080.17			1.47077
$127$	−24.5119			−0.0171266			−0.00856331	−	0.999963i	$-0.502726\pi$
$127$	−24.5119			−0.0171266			−0.00856331	+	0.999963i	$0.502726\pi$
$128$	−981.644	−	981.644i	−0.677859	−	0.677859i
$129$	−2773.19			−1.89276
$130$	31.7766	+	547.375i	0.0214384	+	0.369292i
$131$		−	719.646i		−	0.479967i	−0.970777	−	0.239984i	$-0.922858\pi$
$131$		−	719.646i		−	0.479967i	0.970777	−	0.239984i	$-0.0771421\pi$
$132$	22.4428	+	1292.92i	0.0147984	+	0.852532i
$133$	2324.32			1.51537
$134$	−227.995			−0.146983
$135$	−67.5960	−	67.5960i	−0.0430944	−	0.0430944i
$136$	391.222	+	391.222i	0.246669	+	0.246669i
$137$	−1241.20	+	1241.20i	−0.774037	+	0.774037i	−0.978810	−	0.204773i	$-0.934354\pi$
$137$	−1241.20	+	1241.20i	−0.774037	+	0.774037i	0.204773	+	0.978810i	$0.434354\pi$
$138$	3998.12	+	3998.12i	2.46625	+	2.46625i
$139$			2481.70i			1.51435i	0.653210	+	0.757177i	$0.273422\pi$
$139$			2481.70i			1.51435i	−0.653210	+	0.757177i	$0.726578\pi$
$140$	−290.624			−0.175444
$141$	−3054.99	+	3054.99i	−1.82466	+	1.82466i
$142$	−1960.05			−1.15834
$143$	−128.719	−	1705.18i	−0.0752729	−	0.997163i
$144$	2452.45			1.41924
$145$	259.069	−	259.069i	0.148376	−	0.148376i
$146$	−1083.06			−0.613934
$147$		−	127.030i		−	0.0712739i
$148$	1266.72	+	1266.72i	0.703540	+	0.703540i
$149$	873.774	−	873.774i	0.480418	−	0.480418i	−0.424847	−	0.905265i	$-0.639672\pi$
$149$	873.774	−	873.774i	0.480418	−	0.480418i	0.905265	+	0.424847i	$0.139672\pi$
$150$	−2184.81	−	2184.81i	−1.18926	−	1.18926i
$151$	20.0690	+	20.0690i	0.0108159	+	0.0108159i	0.712494	−	0.701678i	$-0.247566\pi$
$151$	20.0690	+	20.0690i	0.0108159	+	0.0108159i	−0.701678	+	0.712494i	$0.747566\pi$
$152$	1455.98			0.776943
$153$	−1435.47			−0.758505
$154$	2461.69	−	42.7306i	1.28811	−	0.0223593i
$155$			710.122i			0.367990i
$156$	1658.57	−	96.2842i	0.851227	−	0.0494161i
$157$	2414.06			1.22715			0.613576	−	0.789636i	$-0.289730\pi$
$157$	2414.06			1.22715			0.613576	+	0.789636i	$0.289730\pi$
$158$	−1447.12	−	1447.12i	−0.728651	−	0.728651i
$159$	−861.908			−0.429898
$160$	−618.249			−0.305480
$161$	2802.45	−	2802.45i	1.37183	−	1.37183i
$162$	1537.64	−	1537.64i	0.745731	−	0.745731i
$163$	1037.96	−	1037.96i	0.498770	−	0.498770i	−0.412285	−	0.911055i	$-0.635269\pi$
$163$	1037.96	−	1037.96i	0.498770	−	0.498770i	0.911055	+	0.412285i	$0.135269\pi$
$164$	−869.603	−	869.603i	−0.414052	−	0.414052i
$165$	−655.995	−	633.610i	−0.309510	−	0.298948i
$166$			1390.46i			0.650124i
$167$	−1463.70	−	1463.70i	−0.678231	−	0.678231i	0.281369	−	0.959600i	$-0.409211\pi$
$167$	−1463.70	−	1463.70i	−0.678231	−	0.678231i	−0.959600	+	0.281369i	$0.909211\pi$
$168$		−	1713.40i		−	0.786857i
$169$	−2182.24	+	254.227i	−0.993282	+	0.115715i
$170$	544.762			0.245773
$171$	−2671.14	+	2671.14i	−1.19454	+	1.19454i
$172$		−	1699.88i		−	0.753576i
$173$	1187.36			0.521812			0.260906	−	0.965364i	$-0.415979\pi$
$173$	1187.36			0.521812			0.260906	+	0.965364i	$0.415979\pi$
$174$	−2132.27	−	2132.27i	−0.929008	−	0.929008i
$175$	−1531.42	+	1531.42i	−0.661513	+	0.661513i
$176$	2902.24	−	50.3778i	1.24298	−	0.0215760i
$177$	−1330.56	+	1330.56i	−0.565036	+	0.565036i
$178$			1162.72i			0.489606i
$179$		−	1341.99i		−	0.560364i	−0.959947	−	0.280182i	$-0.909605\pi$
$179$		−	1341.99i		−	0.560364i	0.959947	−	0.280182i	$-0.0903949\pi$
$180$	333.989	−	333.989i	0.138300	−	0.138300i
$181$		−	2744.95i		−	1.12724i	−0.826034	−	0.563620i	$-0.809408\pi$
$181$		−	2744.95i		−	1.12724i	0.826034	−	0.563620i	$-0.190592\pi$
$182$	−183.323	−	3157.87i	−0.0746638	−	1.28614i
$183$		−	5178.16i		−	2.09170i
$184$	1755.49	−	1755.49i	0.703349	−	0.703349i
$185$	−1263.47			−0.502122
$186$	5844.67			2.30404
$187$	−1698.75	+	29.4873i	−0.664305	+	0.0115312i
$188$	−1872.62	−	1872.62i	−0.726462	−	0.726462i
$189$	389.969	+	389.969i	0.150085	+	0.150085i
$190$	1013.70	−	1013.70i	0.387059	−	0.387059i
$191$	517.296			0.195970			0.0979848	−	0.995188i	$-0.468760\pi$
$191$	517.296			0.195970			0.0979848	+	0.995188i	$0.468760\pi$
$192$			248.403i			0.0933695i
$193$	−224.441	−	224.441i	−0.0837080	−	0.0837080i	0.664013	−	0.747721i	$-0.268852\pi$
$193$	−224.441	−	224.441i	−0.0837080	−	0.0837080i	−0.747721	+	0.664013i	$0.768852\pi$
$194$	2172.23			0.803903
$195$	−779.137	+	875.175i	−0.286129	+	0.321398i
$196$	77.8657			0.0283767
$197$	−212.541	+	212.541i	−0.0768675	+	0.0768675i	−0.744495	−	0.667628i	$-0.767310\pi$
$197$	−212.541	+	212.541i	−0.0768675	+	0.0768675i	0.667628	+	0.744495i	$0.267310\pi$
$198$	−2779.90	+	2878.12i	−0.997773	+	1.03302i
$199$			3229.43i			1.15039i	0.818015	+	0.575196i	$0.195074\pi$
$199$			3229.43i			1.15039i	−0.818015	+	0.575196i	$0.804926\pi$
$200$	−959.301	+	959.301i	−0.339164	+	0.339164i
$201$	−344.530	−	344.530i	−0.120902	−	0.120902i
$202$	−4216.29	+	4216.29i	−1.46860	+	1.46860i
$203$	−1494.60	+	1494.60i	−0.516751	+	0.516751i
$204$		−	1650.65i		−	0.566512i
$205$	867.373			0.295512
$206$	547.716	+	547.716i	0.185249	+	0.185249i
$207$			6441.24i			2.16279i
$208$	−216.131	−	3723.02i	−0.0720481	−	1.24108i
$209$	−3106.18	+	3215.92i	−1.02803	+	1.06435i
$210$	−1192.92	−	1192.92i	−0.391998	−	0.391998i
$211$			3118.80i			1.01757i	0.860894	+	0.508785i	$0.169905\pi$
$211$			3118.80i			1.01757i	−0.860894	+	0.508785i	$0.830095\pi$
$212$		−	528.325i		−	0.171158i
$213$	−2961.90	−	2961.90i	−0.952798	−	0.952798i
$214$	−1909.45	−	1909.45i	−0.609940	−	0.609940i
$215$	847.763	+	847.763i	0.268916	+	0.268916i
$216$	244.281	+	244.281i	0.0769500	+	0.0769500i
$217$		−	4096.78i		−	1.28160i
$218$			470.831i			0.146279i
$219$	−1636.64	−	1636.64i	−0.504995	−	0.504995i
$220$	388.384	−	402.106i	0.119022	−	0.123227i
$221$	126.507	+	2179.17i	0.0385057	+	0.663288i
$222$			10399.0i			3.14387i
$223$	−3287.43	−	3287.43i	−0.987185	−	0.987185i	0.0127336	−	0.999919i	$-0.495947\pi$
$223$	−3287.43	−	3287.43i	−0.987185	−	0.987185i	−0.999919	+	0.0127336i	$0.995947\pi$
$224$	3566.75			1.06390
$225$		−	3519.87i		−	1.04292i
$226$	−2530.78	+	2530.78i	−0.744890	+	0.744890i
$227$	797.213	−	797.213i	0.233096	−	0.233096i	−0.580887	−	0.813984i	$-0.697294\pi$
$227$	797.213	−	797.213i	0.233096	−	0.233096i	0.813984	+	0.580887i	$0.197294\pi$
$228$	−3071.53	−	3071.53i	−0.892181	−	0.892181i
$229$	3339.44	−	3339.44i	0.963653	−	0.963653i	−0.0357093	−	0.999362i	$-0.511369\pi$
$229$	3339.44	−	3339.44i	0.963653	−	0.963653i	0.999362	+	0.0357093i	$0.0113691\pi$
$230$		−	2444.45i		−	0.700792i
$231$	3784.51	+	3655.37i	1.07793	+	1.04115i
$232$	−936.235	+	936.235i	−0.264943	+	0.264943i
$233$	3605.68			1.01380			0.506901	−	0.862005i	$-0.330791\pi$
$233$	3605.68			1.01380			0.506901	+	0.862005i	$0.330791\pi$
$234$	3839.75	+	3418.39i	1.07270	+	0.954988i
$235$	1867.82			0.518481
$236$	−815.597	−	815.597i	−0.224961	−	0.224961i
$237$		−	4373.58i		−	1.19871i
$238$	−3142.80			−0.855955
$239$	−802.040	+	802.040i	−0.217070	+	0.217070i	−0.807262	−	0.590193i	$-0.799052\pi$
$239$	−802.040	+	802.040i	−0.217070	+	0.217070i	0.590193	+	0.807262i	$0.299052\pi$
$240$	−1406.41	−	1406.41i	−0.378265	−	0.378265i
$241$	−4106.85	−	4106.85i	−1.09770	−	1.09770i	−0.994679	−	0.103020i	$-0.967149\pi$
$241$	−4106.85	−	4106.85i	−1.09770	−	1.09770i	−0.103020	−	0.994679i	$-0.532851\pi$
$242$	−3230.64	+	3463.09i	−0.858154	+	0.919900i
$243$	5432.27			1.43408
$244$	3174.06			0.832781
$245$	−38.8330	+	38.8330i	−0.0101263	+	0.0101263i
$246$		−	7138.92i		−	1.85025i
$247$	4290.41	+	3819.60i	1.10523	+	0.983950i
$248$		−	2566.27i		−	0.657089i
$249$	−2101.17	+	2101.17i	−0.534764	+	0.534764i
$250$			2798.00i			0.707845i
$251$		−	3882.72i		−	0.976396i	−0.872733	−	0.488198i	$-0.837654\pi$
$251$		−	3882.72i		−	0.976396i	0.872733	−	0.488198i	$-0.162346\pi$
$252$	−1926.82	+	1926.82i	−0.481660	+	0.481660i
$253$	132.315	+	7622.61i	0.0328797	+	1.89419i
$254$	61.6736	−	61.6736i	0.0152352	−	0.0152352i
$255$	823.208	+	823.208i	0.202162	+	0.202162i
$256$	5201.09			1.26980
$257$			6446.55i			1.56469i	0.622846	+	0.782344i	$0.285976\pi$
$257$			6446.55i			1.56469i	−0.622846	+	0.782344i	$0.714024\pi$
$258$	6977.52	−	6977.52i	1.68373	−	1.68373i
$259$	7289.14			1.74874
$260$	−536.457	−	477.589i	−0.127960	−	0.113918i
$261$		−	3435.23i		−	0.814696i
$262$	1810.67	+	1810.67i	0.426961	+	0.426961i
$263$			912.812i			0.214017i	0.994258	+	0.107008i	$0.0341272\pi$
$263$			912.812i			0.214017i	−0.994258	+	0.107008i	$0.965873\pi$
$264$	2370.66	+	2289.76i	0.552666	+	0.533807i
$265$	263.485	+	263.485i	0.0610783	+	0.0610783i
$266$	−5848.14	+	5848.14i	−1.34802	+	1.34802i
$267$	−1757.03	+	1757.03i	−0.402728	+	0.402728i
$268$	211.187	−	211.187i	0.0481355	−	0.0481355i
$269$	−5658.62			−1.28257			−0.641287	−	0.767301i	$-0.721599\pi$
$269$	−5658.62			−1.28257			−0.641287	+	0.767301i	$0.721599\pi$
$270$	340.152			0.0766703
$271$	−2930.76	−	2930.76i	−0.656941	−	0.656941i	0.297714	−	0.954655i	$-0.403776\pi$
$271$	−2930.76	−	2930.76i	−0.656941	−	0.656941i	−0.954655	+	0.297714i	$0.903776\pi$
$272$	−3705.24			−0.825968
$273$	4494.94	−	5048.99i	0.996505	−	1.11934i
$274$		−	6245.89i		−	1.37711i
$275$	−72.3046	−	4165.44i	−0.0158550	−	0.913402i
$276$	−7406.76			−1.61534
$277$	4098.08			0.888916			0.444458	−	0.895800i	$-0.353396\pi$
$277$	4098.08			0.888916			0.444458	+	0.895800i	$0.353396\pi$
$278$	−6244.12	−	6244.12i	−1.34711	−	1.34711i
$279$	4708.07	+	4708.07i	1.01027	+	1.01027i
$280$	−523.787	+	523.787i	−0.111794	+	0.111794i
$281$	4392.40	+	4392.40i	0.932486	+	0.932486i	0.997861	−	0.0653747i	$-0.0208243\pi$
$281$	4392.40	+	4392.40i	0.932486	+	0.932486i	−0.0653747	+	0.997861i	$0.520824\pi$
$282$		−	15373.1i		−	3.24629i
$283$	−1309.74			−0.275109			−0.137555	−	0.990494i	$-0.543924\pi$
$283$	−1309.74			−0.275109			−0.137555	+	0.990494i	$0.543924\pi$
$284$	1815.56	−	1815.56i	0.379343	−	0.379343i
$285$	3063.66			0.636756
$286$	4614.21	+	3966.48i	0.953999	+	0.820079i
$287$	−5003.98			−1.02918
$288$	−4098.96	+	4098.96i	−0.838658	+	0.838658i
$289$	−2744.23			−0.558566
$290$			1303.67i			0.263980i
$291$	3282.53	+	3282.53i	0.661255	+	0.661255i
$292$	1003.21	−	1003.21i	0.201057	−	0.201057i
$293$	268.349	+	268.349i	0.0535055	+	0.0535055i	0.733353	−	0.679848i	$-0.237954\pi$
$293$	268.349	+	268.349i	0.0535055	+	0.0535055i	−0.679848	+	0.733353i	$0.737954\pi$
$294$	319.616	+	319.616i	0.0634026	+	0.0634026i
$295$	813.506			0.160556
$296$	4565.99			0.896597
$297$	−1060.71	+	18.4120i	−0.207234	+	0.00359721i
$298$			4396.94i			0.854725i
$299$	9778.33	−	567.659i	1.89129	−	0.109794i
$300$	4047.49			0.778939
$301$	−4890.84	−	4890.84i	−0.936557	−	0.936557i
$302$	−100.990			−0.0192428
$303$	−12742.7			−2.41601
$304$	−6894.74	+	6894.74i	−1.30079	+	1.30079i
$305$	−1582.96	+	1582.96i	−0.297181	+	0.297181i
$306$	3611.75	−	3611.75i	0.674738	−	0.674738i
$307$	3334.91	+	3334.91i	0.619979	+	0.619979i	0.945526	−	0.325547i	$-0.105548\pi$
$307$	3334.91	+	3334.91i	0.619979	+	0.619979i	−0.325547	+	0.945526i	$0.605548\pi$
$308$	−2240.64	+	2319.80i	−0.414520	+	0.429164i
$309$			1655.34i			0.304755i
$310$	−1786.71	−	1786.71i	−0.327350	−	0.327350i
$311$			2958.27i			0.539384i	0.962947	+	0.269692i	$0.0869219\pi$
$311$			2958.27i			0.539384i	−0.962947	+	0.269692i	$0.913078\pi$
$312$	2815.67	−	3162.74i	0.510917	−	0.573894i
$313$	1199.65			0.216639			0.108320	−	0.994116i	$-0.465453\pi$
$313$	1199.65			0.216639			0.108320	+	0.994116i	$0.465453\pi$
$314$	−6073.93	+	6073.93i	−1.09163	+	1.09163i
$315$		−	1921.88i		−	0.343764i
$316$	2680.88			0.477251
$317$	5288.78	+	5288.78i	0.937058	+	0.937058i	0.998133	−	0.0610751i	$-0.0194529\pi$
$317$	5288.78	+	5288.78i	0.937058	+	0.937058i	−0.0610751	+	0.998133i	$0.519453\pi$
$318$	2168.62	−	2168.62i	0.382421	−	0.382421i
$319$	−70.5661	−	4065.28i	−0.0123854	−	0.713518i
$320$	75.9367	−	75.9367i	0.0132656	−	0.0132656i
$321$		−	5770.85i		−	1.00342i
$322$			14102.3i			2.44066i
$323$	4035.65	−	4035.65i	0.695200	−	0.695200i
$324$			2848.57i			0.488438i
$325$	−5343.45	+	310.202i	−0.912004	+	0.0529443i
$326$			5223.16i			0.887375i
$327$	−711.488	+	711.488i	−0.120322	+	0.120322i
$328$	−3134.54			−0.527671
$329$	−10775.7			−1.80572
$330$	3244.73	−	56.3227i	0.541262	−	0.00939534i
$331$	1301.01	+	1301.01i	0.216042	+	0.216042i	0.806828	−	0.590786i	$-0.201182\pi$
$331$	1301.01	+	1301.01i	0.216042	+	0.216042i	−0.590786	+	0.806828i	$0.701182\pi$
$332$	−1287.96	−	1287.96i	−0.212909	−	0.212909i
$333$	−8376.77	+	8376.77i	−1.37851	+	1.37851i
$334$	7365.53			1.20666
$335$			210.646i			0.0343546i
$336$	8113.77	+	8113.77i	1.31739	+	1.31739i
$337$	2082.31			0.336590			0.168295	−	0.985737i	$-0.446174\pi$
$337$	2082.31			0.336590			0.168295	+	0.985737i	$0.446174\pi$
$338$	4851.01	−	6130.31i	0.780651	−	0.986524i
$339$	−7648.69			−1.22543
$340$	−504.602	+	504.602i	−0.0804879	+	0.0804879i
$341$	5668.29	+	5474.86i	0.900161	+	0.869444i
$342$		−	13441.5i		−	2.12524i
$343$	−4375.91	+	4375.91i	−0.688854	+	0.688854i
$344$	−3063.68	−	3063.68i	−0.480181	−	0.480181i
$345$	3693.88	−	3693.88i	0.576441	−	0.576441i
$346$	−2987.48	+	2987.48i	−0.464185	+	0.464185i
$347$			8822.61i			1.36491i	0.730929	+	0.682453i	$0.239087\pi$
$347$			8822.61i			1.36491i	−0.730929	+	0.682453i	$0.760913\pi$
$348$	3950.17			0.608480
$349$	678.351	+	678.351i	0.104044	+	0.104044i	0.757212	−	0.653169i	$-0.226561\pi$
$349$	678.351	+	678.351i	0.104044	+	0.104044i	−0.653169	+	0.757212i	$0.726561\pi$
$350$		−	7706.33i		−	1.17692i
$351$	78.9913	+	1360.68i	0.0120121	+	0.206917i
$352$	−4766.54	+	4934.94i	−0.721754	+	0.747253i
$353$	574.813	+	574.813i	0.0866692	+	0.0866692i	0.749112	−	0.662443i	$-0.230480\pi$
$353$	574.813	+	574.813i	0.0866692	+	0.0866692i	−0.662443	+	0.749112i	$0.730480\pi$
$354$		−	6695.57i		−	1.00527i
$355$			1810.90i			0.270740i
$356$	−1077.01	−	1077.01i	−0.160341	−	0.160341i
$357$	−4749.18	−	4749.18i	−0.704071	−	0.704071i
$358$	3376.54	+	3376.54i	0.498479	+	0.498479i
$359$	−1313.51	−	1313.51i	−0.193103	−	0.193103i	0.603932	−	0.797036i	$-0.293600\pi$
$359$	−1313.51	−	1313.51i	−0.193103	−	0.193103i	−0.797036	+	0.603932i	$0.793600\pi$
$360$		−	1203.89i		−	0.176251i
$361$		−	8160.13i		−	1.18970i
$362$	6906.47	+	6906.47i	1.00275	+	1.00275i
$363$	−10115.1	+	351.266i	−1.46255	+	0.0507898i
$364$	3094.88	+	2755.27i	0.445648	+	0.396745i
$365$			1000.64i			0.143496i
$366$	13028.6	+	13028.6i	1.86070	+	1.86070i
$367$	1158.32			0.164751			0.0823756	−	0.996601i	$-0.473749\pi$
$367$	1158.32			0.164751			0.0823756	+	0.996601i	$0.473749\pi$
$368$			16626.1i			2.35515i
$369$	5750.64	−	5750.64i	0.811290	−	0.811290i
$370$	3178.98	−	3178.98i	0.446669	−	0.446669i
$371$	−1520.08	−	1520.08i	−0.212718	−	0.212718i
$372$	−5413.80	+	5413.80i	−0.754550	+	0.754550i
$373$			9221.21i			1.28004i	0.768357	+	0.640022i	$0.221075\pi$
$373$			9221.21i			1.28004i	−0.768357	+	0.640022i	$0.778925\pi$
$374$	4199.98	−	4348.36i	0.580684	−	0.601199i
$375$	−4228.15	+	4228.15i	−0.582242	+	0.582242i
$376$	−6749.99			−0.925809
$377$	−5214.97	+	302.743i	−0.712426	+	0.0413583i
$378$	−1962.38			−0.267020
$379$	−6619.12	−	6619.12i	−0.897101	−	0.897101i	0.0980775	−	0.995179i	$-0.468731\pi$
$379$	−6619.12	−	6619.12i	−0.897101	−	0.897101i	−0.995179	+	0.0980775i	$0.968731\pi$
$380$			1877.93i			0.253516i
$381$	186.394			0.0250636
$382$	−1301.55	+	1301.55i	−0.174327	+	0.174327i
$383$	−5771.44	−	5771.44i	−0.769991	−	0.769991i	0.208113	−	0.978105i	$-0.433268\pi$
$383$	−5771.44	−	5771.44i	−0.769991	−	0.769991i	−0.978105	+	0.208113i	$0.933268\pi$
$384$	7464.63	+	7464.63i	0.991999	+	0.991999i
$385$	−39.4790	−	2274.37i	−0.00522607	−	0.301072i
$386$	1129.42			0.148927
$387$	11241.2			1.47655
$388$	−2012.10	+	2012.10i	−0.263270	+	0.263270i
$389$			7761.72i			1.01166i	0.862634	+	0.505829i	$0.168813\pi$
$389$			7761.72i			1.01166i	−0.862634	+	0.505829i	$0.831187\pi$
$390$	−241.636	−	4162.36i	−0.0313736	−	0.540433i
$391$		−	9731.65i		−	1.25870i
$392$	140.336	−	140.336i	0.0180818	−	0.0180818i
$393$			5472.34i			0.702399i
$394$		−	1069.53i		−	0.136757i
$395$	−1337.00	+	1337.00i	−0.170309	+	0.170309i
$396$	−90.9728	−	5240.91i	−0.0115443	−	0.665065i
$397$	8667.74	−	8667.74i	1.09577	−	1.09577i	0.100872	−	0.994899i	$-0.467837\pi$
$397$	8667.74	−	8667.74i	1.09577	−	1.09577i	0.994899	−	0.100872i	$-0.0321634\pi$
$398$	−8125.45	−	8125.45i	−1.02335	−	1.02335i
$399$	−17674.6			−2.21764
$400$		−	9085.48i		−	1.13568i
$401$	150.368	−	150.368i	0.0187257	−	0.0187257i	−0.697682	−	0.716408i	$-0.745785\pi$
$401$	150.368	−	150.368i	0.0187257	−	0.0187257i	0.716408	+	0.697682i	$0.245785\pi$
$402$	1733.72			0.215100
$403$	6732.33	−	7562.16i	0.832162	−	0.934735i
$404$		−	7810.94i		−	0.961902i
$405$	−1420.63	−	1420.63i	−0.174301	−	0.174301i
$406$		−	7521.03i		−	0.919366i
$407$	−9741.07	+	10085.2i	−1.18636	+	1.22827i
$408$	−2974.94	−	2974.94i	−0.360984	−	0.360984i
$409$	1929.55	−	1929.55i	0.233277	−	0.233277i	−0.580782	−	0.814059i	$-0.697253\pi$
$409$	1929.55	−	1929.55i	0.233277	−	0.233277i	0.814059	+	0.580782i	$0.197253\pi$
$410$	−2182.37	+	2182.37i	−0.262876	+	0.262876i
$411$	9438.36	−	9438.36i	1.13275	−	1.13275i
$412$	−1014.68			−0.121334
$413$	−4693.21			−0.559171
$414$	−16206.6	−	16206.6i	−1.92394	−	1.92394i
$415$	1284.65			0.151955
$416$	6583.79	+	5861.32i	0.775954	+	0.690805i
$417$		−	18871.4i		−	2.21615i
$418$	−276.114	−	15906.8i	−0.0323090	−	1.86131i
$419$	3486.59			0.406518			0.203259	−	0.979125i	$-0.434847\pi$
$419$	3486.59			0.406518			0.203259	+	0.979125i	$0.434847\pi$
$420$	2209.96			0.256751
$421$	−2899.83	−	2899.83i	−0.335699	−	0.335699i	0.519047	−	0.854746i	$-0.326287\pi$
$421$	−2899.83	−	2899.83i	−0.335699	−	0.335699i	−0.854746	+	0.519047i	$0.826287\pi$
$422$	−7847.11	−	7847.11i	−0.905193	−	0.905193i
$423$	12383.5	−	12383.5i	1.42342	−	1.42342i
$424$	−952.191	−	952.191i	−0.109062	−	0.109062i
$425$			5317.94i			0.606960i
$426$	14904.7			1.69515
$427$	9132.30	−	9132.30i	1.03499	−	1.03499i
$428$	3537.37			0.399498
$429$	978.806	+	12966.5i	0.110157	+	1.45928i
$430$	−4266.05			−0.478436
$431$	10721.2	−	10721.2i	1.19819	−	1.19819i	0.223485	−	0.974707i	$-0.428257\pi$
$431$	10721.2	−	10721.2i	1.19819	−	1.19819i	0.974707	−	0.223485i	$-0.0717434\pi$
$432$	−2313.57			−0.257666
$433$			7203.74i			0.799514i	0.916621	+	0.399757i	$0.130906\pi$
$433$			7203.74i			0.799514i	−0.916621	+	0.399757i	$0.869094\pi$
$434$	10307.8	+	10307.8i	1.14007	+	1.14007i
$435$	−1970.02	+	1970.02i	−0.217138	+	0.217138i
$436$	−436.122	−	436.122i	−0.0479047	−	0.0479047i
$437$	−18108.7	−	18108.7i	−1.98228	−	1.98228i
$438$	8235.78			0.898449
$439$	−4277.16			−0.465006			−0.232503	−	0.972596i	$-0.574692\pi$
$439$	−4277.16			−0.465006			−0.232503	+	0.972596i	$0.574692\pi$
$440$	−24.7301	−	1424.69i	−0.00267945	−	0.154362i
$441$			514.922i			0.0556011i
$442$	−5801.23	−	5164.63i	−0.624290	−	0.555784i
$443$	3800.38			0.407588			0.203794	−	0.979014i	$-0.434673\pi$
$443$	3800.38			0.407588			0.203794	+	0.979014i	$0.434673\pi$
$444$	−9632.43	−	9632.43i	−1.02958	−	1.02958i
$445$	1074.25			0.114436
$446$	16542.8			1.75633
$447$	−6644.36	+	6644.36i	−0.703059	+	0.703059i
$448$	−438.088	+	438.088i	−0.0462002	+	0.0462002i
$449$	6084.89	−	6084.89i	0.639563	−	0.639563i	−0.310885	−	0.950448i	$-0.600625\pi$
$449$	6084.89	−	6084.89i	0.639563	−	0.639563i	0.950448	+	0.310885i	$0.100625\pi$
$450$	8856.21	+	8856.21i	0.927747	+	0.927747i
$451$	6687.22	−	6923.48i	0.698202	−	0.722869i
$452$		−	4688.42i		−	0.487887i
$453$	−152.609	−	152.609i	−0.0158283	−	0.0158283i
$454$			4011.68i			0.414708i
$455$	−2917.57	+	169.373i	−0.300611	+	0.0174513i
$456$	−11071.6			−1.13700
$457$	−10635.7	+	10635.7i	−1.08866	+	1.08866i	−0.0929928	+	0.995667i	$0.529643\pi$
$457$	−10635.7	+	10635.7i	−1.08866	+	1.08866i	−0.995667	+	0.0929928i	$0.970357\pi$
$458$			16804.5i			1.71446i
$459$	1354.19			0.137708
$460$	2264.24	+	2264.24i	0.229502	+	0.229502i
$461$	10010.7	−	10010.7i	1.01137	−	1.01137i	0.0114374	−	0.999935i	$-0.496359\pi$
$461$	10010.7	−	10010.7i	1.01137	−	1.01137i	0.999935	−	0.0114374i	$-0.00364071\pi$
$462$	−18719.2	+	324.932i	−1.88506	+	0.0327213i
$463$	−4886.66	+	4886.66i	−0.490502	+	0.490502i	−0.908464	−	0.417962i	$-0.862744\pi$
$463$	−4886.66	+	4886.66i	−0.490502	+	0.490502i	0.417962	+	0.908464i	$0.362744\pi$
$464$		−	8867.02i		−	0.887158i
$465$		−	5399.92i		−	0.538527i
$466$	−9072.11	+	9072.11i	−0.901840	+	0.901840i
$467$			2632.42i			0.260844i	0.991459	+	0.130422i	$0.0416332\pi$
$467$			2632.42i			0.260844i	−0.991459	+	0.130422i	$0.958367\pi$
$468$	−6723.07	+	390.292i	−0.664047	+	0.0385497i
$469$		−	1215.24i		−	0.119647i
$470$	−4699.55	+	4699.55i	−0.461222	+	0.461222i
$471$	−18357.0			−1.79585
$472$	−2939.88			−0.286692
$473$	13303.0	−	230.916i	1.29318	−	0.0224472i
$474$	11004.2	+	11004.2i	1.06633	+	1.06633i
$475$	9895.66	+	9895.66i	0.955882	+	0.955882i
$476$	2911.11	−	2911.11i	0.280316	−	0.280316i
$477$	3493.78			0.335365
$478$		−	4035.97i		−	0.386194i
$479$	8667.82	+	8667.82i	0.826812	+	0.826812i	0.987074	−	0.160263i	$-0.0512341\pi$
$479$	8667.82	+	8667.82i	0.826812	+	0.826812i	−0.160263	+	0.987074i	$0.551234\pi$
$480$	4701.29			0.447049
$481$	13454.9	+	11978.4i	1.27545	+	1.13548i
$482$	20666.2			1.95295
$483$	−21310.5	+	21310.5i	−2.00758	+	2.00758i
$484$	−215.316	−	6200.27i	−0.0202213	−	0.582294i
$485$		−	2006.94i		−	0.187897i
$486$	−13667.9	+	13667.9i	−1.27570	+	1.27570i
$487$	−1030.75	−	1030.75i	−0.0959093	−	0.0959093i	0.657524	−	0.753433i	$-0.271604\pi$
$487$	−1030.75	−	1030.75i	−0.0959093	−	0.0959093i	−0.753433	+	0.657524i	$0.771604\pi$
$488$	5720.57	−	5720.57i	0.530651	−	0.530651i
$489$	−7892.89	+	7892.89i	−0.729915	+	0.729915i
$490$		−	195.413i		−	0.0180160i
$491$	8778.11			0.806824			0.403412	−	0.915019i	$-0.367824\pi$
$491$	8778.11			0.806824			0.403412	+	0.915019i	$0.367824\pi$
$492$	6612.64	+	6612.64i	0.605937	+	0.605937i
$493$			5190.08i			0.474136i
$494$	−20405.3	+	1184.59i	−1.85846	+	0.107889i
$495$	2659.10	+	2568.37i	0.241450	+	0.233211i
$496$	12152.5	+	12152.5i	1.10013	+	1.10013i
$497$		−	10447.3i		−	0.942909i
$498$		−	10573.4i		−	0.951412i
$499$	4041.61	+	4041.61i	0.362580	+	0.362580i	0.864762	−	0.502182i	$-0.167469\pi$
$499$	4041.61	+	4041.61i	0.362580	+	0.362580i	−0.502182	+	0.864762i	$0.667469\pi$
$500$	−2591.73	−	2591.73i	−0.231812	−	0.231812i
$501$	11130.3	+	11130.3i	0.992543	+	0.992543i
$502$	9769.19	+	9769.19i	0.868566	+	0.868566i
$503$			15972.6i			1.41587i	0.706279	+	0.707933i	$0.250372\pi$
$503$			15972.6i			1.41587i	−0.706279	+	0.707933i	$0.749628\pi$
$504$			6945.36i			0.613831i
$505$	3895.45	+	3895.45i	0.343258	+	0.343258i
$506$	−19511.9	−	18846.1i	−1.71425	−	1.65575i
$507$	16594.2	−	1933.19i	1.45360	−	0.169342i
$508$			114.254i			0.00997874i
$509$	−2379.75	−	2379.75i	−0.207231	−	0.207231i	0.595859	−	0.803089i	$-0.296812\pi$
$509$	−2379.75	−	2379.75i	−0.207231	−	0.207231i	−0.803089	+	0.595859i	$0.796812\pi$
$510$	−4142.49			−0.359671
$511$		−	5772.81i		−	0.499754i
$512$	−5233.13	+	5233.13i	−0.451707	+	0.451707i
$513$	2519.88	−	2519.88i	0.216872	−	0.216872i
$514$	−16219.9	−	16219.9i	−1.39189	−	1.39189i
$515$	506.038	−	506.038i	0.0432984	−	0.0432984i
$516$			12926.3i			1.10281i
$517$	14400.4	−	14909.2i	1.22501	−	1.26829i
$518$	−18339.9	+	18339.9i	−1.55562	+	1.55562i
$519$	−9028.95			−0.763636
$520$	−1827.60	+	106.097i	−0.154126	+	0.00894743i
$521$	11760.8			0.988961			0.494481	−	0.869189i	$-0.335358\pi$
$521$	11760.8			0.988961			0.494481	+	0.869189i	$0.335358\pi$
$522$	8643.27	+	8643.27i	0.724724	+	0.724724i
$523$			1709.27i			0.142908i	0.997444	+	0.0714541i	$0.0227640\pi$
$523$			1709.27i			0.142908i	−0.997444	+	0.0714541i	$0.977236\pi$
$524$	−3354.38			−0.279651
$525$	11645.3	−	11645.3i	0.968079	−	0.968079i
$526$	−2296.69	−	2296.69i	−0.190381	−	0.190381i
$527$	−7113.13	−	7113.13i	−0.587956	−	0.587956i
$528$	−22069.3	+	383.083i	−1.81902	+	0.0315749i
$529$	−31500.7			−2.58903
$530$	−1325.89			−0.108666
$531$	5393.50	−	5393.50i	0.440787	−	0.440787i
$532$		−	10834.0i		−	0.882922i
$533$	−9236.74	−	8223.14i	−0.750633	−	0.668262i
$534$		−	8841.60i		−	0.716505i
$535$	−1764.15	+	1764.15i	−0.142562	+	0.142562i
$536$		−	761.239i		−	0.0613442i
$537$			10204.8i			0.820054i
$538$	14237.5	−	14237.5i	1.14093	−	1.14093i
$539$	10.5775	+	609.363i	0.000845275	+	0.0486959i
$540$	−315.076	+	315.076i	−0.0251087	+	0.0251087i
$541$	−8796.06	−	8796.06i	−0.699024	−	0.699024i	0.265176	−	0.964200i	$-0.414570\pi$
$541$	−8796.06	−	8796.06i	−0.699024	−	0.699024i	−0.964200	+	0.265176i	$0.914570\pi$
$542$	14748.0			1.16878
$543$			20873.2i			1.64964i
$544$	6192.85	−	6192.85i	0.488082	−	0.488082i
$545$	435.003			0.0341899
$546$	1394.03	+	24013.1i	0.109265	+	1.88217i
$547$			7953.52i			0.621696i	0.950460	+	0.310848i	$0.100613\pi$
$547$			7953.52i			0.621696i	−0.950460	+	0.310848i	$0.899387\pi$
$548$	5785.44	+	5785.44i	0.450988	+	0.450988i
$549$			20989.9i			1.63174i
$550$	10662.4	+	10298.6i	0.826633	+	0.798425i
$551$	9657.72	+	9657.72i	0.746702	+	0.746702i
$552$	−13349.1	+	13349.1i	−1.02930	+	1.02930i
$553$	7713.33	−	7713.33i	0.593136	−	0.593136i
$554$	−10311.0	+	10311.0i	−0.790747	+	0.790747i
$555$	9607.73			0.734820
$556$	11567.6			0.882330
$557$	14061.2	+	14061.2i	1.06964	+	1.06964i	0.997386	+	0.0722577i	$0.0230204\pi$
$557$	14061.2	+	14061.2i	1.06964	+	1.06964i	0.0722577	+	0.997386i	$0.476980\pi$
$558$	−23691.6			−1.79740
$559$	−990.678	−	17065.1i	−0.0749575	−	1.29120i
$560$		−	4960.75i		−	0.374340i
$561$	12917.7	−	224.228i	0.972164	−	0.0168750i
$562$	−22103.1			−1.65901
$563$	856.834			0.0641408			0.0320704	−	0.999486i	$-0.489790\pi$
$563$	856.834			0.0641408			0.0320704	+	0.999486i	$0.489790\pi$
$564$	14239.8	+	14239.8i	1.06313	+	1.06313i
$565$	2338.20	+	2338.20i	0.174104	+	0.174104i
$566$	3295.39	−	3295.39i	0.244727	−	0.244727i
$567$	8195.80	+	8195.80i	0.607039	+	0.607039i
$568$		−	6544.30i		−	0.483438i
$569$	−19837.4			−1.46156			−0.730781	−	0.682612i	$-0.760844\pi$
$569$	−19837.4			−1.46156			−0.730781	+	0.682612i	$0.760844\pi$
$570$	−7708.36	+	7708.36i	−0.566435	+	0.566435i
$571$	14647.6			1.07352			0.536761	−	0.843734i	$-0.319648\pi$
$571$	14647.6			1.07352			0.536761	+	0.843734i	$0.319648\pi$
$572$	−7948.12	+	599.980i	−0.580992	+	0.0438574i
$573$	−3933.62			−0.286788
$574$	12590.3	−	12590.3i	0.915523	−	0.915523i
$575$	23862.6			1.73068
$576$		−	1006.91i		−	0.0728380i
$577$	−11584.3	−	11584.3i	−0.835804	−	0.835804i	0.152499	−	0.988304i	$-0.451268\pi$
$577$	−11584.3	−	11584.3i	−0.835804	−	0.835804i	−0.988304	+	0.152499i	$0.951268\pi$
$578$	6904.67	−	6904.67i	0.496880	−	0.496880i
$579$	1706.70	+	1706.70i	0.122501	+	0.122501i
$580$	−1207.56	−	1207.56i	−0.0864507	−	0.0864507i
$581$	−7411.31			−0.529214
$582$	−16518.1			−1.17646
$583$	4134.57	−	71.7688i	0.293716	−	0.00509839i
$584$		−	3616.15i		−	0.256228i
$585$	3158.27	−	3547.56i	0.223211	−	0.250724i
$586$	−1350.37			−0.0951930
$587$	−6173.04	−	6173.04i	−0.434052	−	0.434052i	0.455952	−	0.890004i	$-0.349299\pi$
$587$	−6173.04	−	6173.04i	−0.434052	−	0.434052i	−0.890004	+	0.455952i	$0.849299\pi$
$588$	−592.107			−0.0415274
$589$	−26472.3			−1.85190
$590$	−2046.83	+	2046.83i	−0.142825	+	0.142825i
$591$	1616.20	−	1616.20i	0.112490	−	0.112490i
$592$	−21622.1	+	21622.1i	−1.50112	+	1.50112i
$593$	10246.1	+	10246.1i	0.709542	+	0.709542i	0.966439	−	0.256897i	$-0.0827002\pi$
$593$	10246.1	+	10246.1i	0.709542	+	0.709542i	−0.256897	+	0.966439i	$0.582700\pi$
$594$	2622.48	−	2715.13i	0.181148	−	0.187548i
$595$			2903.65i			0.200064i
$596$	−4072.80	−	4072.80i	−0.279913	−	0.279913i
$597$		−	24557.3i		−	1.68352i
$598$	−23174.6	+	26031.2i	−1.58475	+	1.78009i
$599$	7429.11			0.506754			0.253377	−	0.967368i	$-0.418459\pi$
$599$	7429.11			0.506754			0.253377	+	0.967368i	$0.418459\pi$
$600$	7294.72	−	7294.72i	0.496343	−	0.496343i
$601$			11834.7i			0.803241i	0.915806	+	0.401620i	$0.131553\pi$
$601$			11834.7i			0.803241i	−0.915806	+	0.401620i	$0.868447\pi$
$602$	24611.4			1.66625
$603$	1396.57	+	1396.57i	0.0943162	+	0.0943162i
$604$	93.5450	−	93.5450i	0.00630181	−	0.00630181i
$605$	3199.57	+	2984.80i	0.215010	+	0.200578i
$606$	32061.6	−	32061.6i	2.14920	−	2.14920i
$607$		−	9853.03i		−	0.658850i	−0.944182	−	0.329425i	$-0.893145\pi$
$607$		−	9853.03i		−	0.658850i	0.944182	−	0.329425i	$-0.106855\pi$
$608$		−	23047.4i		−	1.53733i
$609$	11365.3	−	11365.3i	0.756230	−	0.756230i
$610$		−	7965.67i		−	0.528722i
$611$	−19890.6	−	17707.9i	−1.31700	−	1.17248i
$612$			6690.97i			0.441939i
$613$	17179.3	−	17179.3i	1.13192	−	1.13192i	0.142062	−	0.989858i	$-0.454627\pi$
$613$	17179.3	−	17179.3i	1.13192	−	1.13192i	0.989858	−	0.142062i	$-0.0453732\pi$
$614$	−16781.7			−1.10302
$615$	−6595.68			−0.432461
$616$	142.671	+	8219.20i	0.00933176	+	0.537599i
$617$	−304.093	−	304.093i	−0.0198417	−	0.0198417i	0.697116	−	0.716958i	$-0.254466\pi$
$617$	−304.093	−	304.093i	−0.0198417	−	0.0198417i	−0.716958	+	0.697116i	$0.754466\pi$
$618$	−4164.95	−	4164.95i	−0.271098	−	0.271098i
$619$	−5720.38	+	5720.38i	−0.371440	+	0.371440i	−0.868002	−	0.496562i	$-0.834596\pi$
$619$	−5720.38	+	5720.38i	−0.371440	+	0.371440i	0.496562	+	0.868002i	$0.334596\pi$
$620$	3309.99			0.214407
$621$		−	6076.48i		−	0.392658i
$622$	−7443.21	−	7443.21i	−0.479816	−	0.479816i
$623$	−6197.46			−0.398549
$624$	1643.51	+	28310.6i	0.105437	+	1.81624i
$625$	−11689.0			−0.748094
$626$	−3018.39	+	3018.39i	−0.192714	+	0.192714i
$627$	23620.0	−	24454.5i	1.50445	−	1.55761i
$628$		−	11252.3i		−	0.714994i
$629$	12655.9	−	12655.9i	0.802265	−	0.802265i
$630$	4835.57	+	4835.57i	0.305800	+	0.305800i
$631$	−21995.4	+	21995.4i	−1.38768	+	1.38768i	−0.557496	+	0.830180i	$0.688238\pi$
$631$	−21995.4	+	21995.4i	−1.38768	+	1.38768i	−0.830180	+	0.557496i	$0.811762\pi$
$632$	4831.71	−	4831.71i	0.304106	−	0.304106i
$633$		−	23716.0i		−	1.48914i
$634$	−26613.8			−1.66714
$635$	−56.9805	−	56.9805i	−0.00356095	−	0.00356095i
$636$			4017.49i			0.250478i
$637$	781.694	−	45.3795i	0.0486214	−	0.00282261i
$638$	10406.1	+	10051.0i	0.645737	+	0.623702i
$639$	12006.2	+	12006.2i	0.743282	+	0.743282i
$640$		−	4563.87i		−	0.281879i
$641$			7356.76i			0.453314i	0.973975	+	0.226657i	$0.0727797\pi$
$641$			7356.76i			0.453314i	−0.973975	+	0.226657i	$0.927220\pi$
$642$	14519.8	+	14519.8i	0.892605	+	0.892605i
$643$	11911.8	+	11911.8i	0.730567	+	0.730567i	0.970732	−	0.240165i	$-0.0772016\pi$
$643$	11911.8	+	11911.8i	0.730567	+	0.730567i	−0.240165	+	0.970732i	$0.577202\pi$
$644$	−13062.7	−	13062.7i	−0.799289	−	0.799289i
$645$	−6446.57	−	6446.57i	−0.393540	−	0.393540i
$646$			20307.9i			1.23685i
$647$			11451.4i			0.695831i	0.937526	+	0.347916i	$0.113110\pi$
$647$			11451.4i			0.695831i	−0.937526	+	0.347916i	$0.886890\pi$
$648$	5133.93	+	5133.93i	0.311235	+	0.311235i
$649$	6271.92	−	6493.51i	0.379344	−	0.392746i
$650$	12664.0	−	14225.0i	0.764188	−	0.858382i
$651$			31152.8i			1.87553i
$652$	−4838.11	−	4838.11i	−0.290606	−	0.290606i
$653$	19162.7			1.14838			0.574191	−	0.818722i	$-0.305317\pi$
$653$	19162.7			1.14838			0.574191	+	0.818722i	$0.305317\pi$
$654$		−	3580.30i		−	0.214069i
$655$	1672.89	−	1672.89i	0.0997943	−	0.0997943i
$656$	14843.5	−	14843.5i	0.883449	−	0.883449i
$657$	6634.19	+	6634.19i	0.393949	+	0.393949i
$658$	27112.3	−	27112.3i	1.60630	−	1.60630i
$659$		−	4110.77i		−	0.242994i	−0.992592	−	0.121497i	$-0.961231\pi$
$659$		−	4110.77i		−	0.242994i	0.992592	−	0.121497i	$-0.0387695\pi$
$660$	−2953.36	+	3057.70i	−0.174181	+	0.180334i
$661$	17020.6	−	17020.6i	1.00155	−	1.00155i	0.00154902	−	0.999999i	$-0.499507\pi$
$661$	17020.6	−	17020.6i	1.00155	−	1.00155i	0.999999	−	0.00154902i	$-0.000493069\pi$
$662$	−6546.85			−0.384366
$663$	−961.983	−	16570.9i	−0.0563504	−	0.970677i
$664$	−4642.52			−0.271333
$665$	5403.12	+	5403.12i	0.315074	+	0.315074i
$666$		−	42153.0i		−	2.45255i
$667$	23288.8			1.35194
$668$	−6822.54	+	6822.54i	−0.395168	+	0.395168i
$669$	24998.3	+	24998.3i	1.44468	+	1.44468i
$670$	−529.998	−	529.998i	−0.0305606	−	0.0305606i
$671$	431.172	+	24839.6i	0.0248066	+	1.42910i
$672$	−27122.3			−1.55694
$673$	−11081.9			−0.634733			−0.317367	−	0.948303i	$-0.602799\pi$
$673$	−11081.9			−0.634733			−0.317367	+	0.948303i	$0.602799\pi$
$674$	−5239.23	+	5239.23i	−0.299418	+	0.299418i
$675$			3320.55i			0.189345i
$676$	1184.99	+	10171.8i	0.0674210	+	0.578731i
$677$		−	22412.8i		−	1.27237i	−0.771538	−	0.636183i	$-0.780512\pi$
$677$		−	22412.8i		−	1.27237i	0.771538	−	0.636183i	$-0.219488\pi$
$678$	19244.6	−	19244.6i	1.09009	−	1.09009i
$679$			11578.3i			0.654392i
$680$			1818.87i			0.102574i
$681$	−6062.18	+	6062.18i	−0.341121	+	0.341121i
$682$	−28036.9	+	486.670i	−1.57417	+	0.0273249i
$683$	−5587.55	+	5587.55i	−0.313033	+	0.313033i	−0.846084	−	0.533050i	$-0.821046\pi$
$683$	−5587.55	+	5587.55i	−0.313033	+	0.313033i	0.533050	+	0.846084i	$0.321046\pi$
$684$	12450.6	+	12450.6i	0.695995	+	0.695995i
$685$	−5770.60			−0.321874
$686$		−	22020.1i		−	1.22556i
$687$	−25393.8	+	25393.8i	−1.41024	+	1.41024i
$688$	29015.9			1.60788
$689$	−307.903	−	5303.85i	−0.0170249	−	0.293266i
$690$			18588.1i			1.02556i
$691$	−8441.72	−	8441.72i	−0.464744	−	0.464744i	0.435463	−	0.900207i	$-0.356585\pi$
$691$	−8441.72	−	8441.72i	−0.464744	−	0.464744i	−0.900207	+	0.435463i	$0.856585\pi$
$692$		−	5534.49i		−	0.304031i
$693$	−15340.7	−	14817.2i	−0.840901	−	0.812206i
$694$	−22198.2	−	22198.2i	−1.21417	−	1.21417i
$695$	−5768.97	+	5768.97i	−0.314863	+	0.314863i
$696$	7119.33	−	7119.33i	0.387726	−	0.387726i
$697$	−8688.27	+	8688.27i	−0.472154	+	0.472154i
$698$	−3413.55			−0.185107
$699$	−27418.3			−1.48363
$700$	7138.22	+	7138.22i	0.385427	+	0.385427i
$701$	2181.87			0.117558			0.0587790	−	0.998271i	$-0.481279\pi$
$701$	2181.87			0.117558			0.0587790	+	0.998271i	$0.481279\pi$
$702$	−3622.31	−	3224.82i	−0.194751	−	0.173380i
$703$		−	47100.4i		−	2.52692i
$704$	−20.6839	−	1191.59i	−0.00110732	−	0.0637922i
$705$	−14203.3			−0.758761
$706$	−2892.53			−0.154195
$707$	−22473.3	−	22473.3i	−1.19547	−	1.19547i
$708$	6201.97	+	6201.97i	0.329215	+	0.329215i
$709$	−14205.1	+	14205.1i	−0.752446	+	0.752446i	−0.974935	−	0.222489i	$-0.928582\pi$
$709$	−14205.1	+	14205.1i	−0.752446	+	0.752446i	0.222489	+	0.974935i	$0.428582\pi$
$710$	−4556.35	−	4556.35i	−0.240840	−	0.240840i
$711$			17728.5i			0.935122i
$712$	−3882.15			−0.204340
$713$	−31917.9	+	31917.9i	−1.67649	+	1.67649i
$714$	23898.5			1.25263
$715$	3664.65	−	4263.09i	0.191678	−	0.222980i
$716$	−6255.24			−0.326493
$717$	6098.88	−	6098.88i	0.317666	−	0.317666i
$718$	6609.73			0.343555
$719$			17317.5i			0.898241i	0.893471	+	0.449120i	$0.148263\pi$
$719$			17317.5i			0.898241i	−0.893471	+	0.449120i	$0.851737\pi$
$720$	5700.96	+	5700.96i	0.295087	+	0.295087i
$721$	−2919.39	+	2919.39i	−0.150796	+	0.150796i
$722$	20531.4	+	20531.4i	1.05831	+	1.05831i
$723$	31229.3	+	31229.3i	1.60641	+	1.60641i
$724$	−12794.6			−0.656781
$725$	−12726.4			−0.651925
$726$	24566.4	−	26334.1i	1.25585	−	1.34621i
$727$			773.727i			0.0394717i	0.999805	+	0.0197359i	$0.00628253\pi$
$727$			773.727i			0.0394717i	−0.999805	+	0.0197359i	$0.993717\pi$
$728$	10543.6	−	612.087i	0.536776	−	0.0311613i
$729$	−24807.7			−1.26036
$730$	−2517.67	−	2517.67i	−0.127648	−	0.127648i
$731$	−16983.7			−0.859322
$732$	−24136.2			−1.21872
$733$	−7514.82	+	7514.82i	−0.378672	+	0.378672i	−0.870623	−	0.491951i	$-0.836284\pi$
$733$	−7514.82	+	7514.82i	−0.378672	+	0.378672i	0.491951	+	0.870623i	$0.336284\pi$
$734$	−2914.40	+	2914.40i	−0.146557	+	0.146557i
$735$	295.294	−	295.294i	0.0148192	−	0.0148192i
$736$	−27788.5	−	27788.5i	−1.39171	−	1.39171i
$737$	1681.40	+	1624.02i	0.0840368	+	0.0811692i
$738$			28937.9i			1.44339i
$739$	1071.38	+	1071.38i	0.0533304	+	0.0533304i	0.733269	−	0.679939i	$-0.237994\pi$
$739$	1071.38	+	1071.38i	0.0533304	+	0.0533304i	−0.679939	+	0.733269i	$0.737994\pi$
$740$			5889.26i			0.292559i
$741$	−32625.2	−	29045.1i	−1.61743	−	1.43994i
$742$	7649.22			0.378452
$743$	−3865.34	+	3865.34i	−0.190855	+	0.190855i	−0.796066	−	0.605210i	$-0.793089\pi$
$743$	−3865.34	+	3865.34i	−0.190855	+	0.190855i	0.605210	+	0.796066i	$0.293089\pi$
$744$			19514.4i			0.961604i
$745$	4062.36			0.199776
$746$	−23201.2	−	23201.2i	−1.13868	−	1.13868i
$747$	8517.18	−	8517.18i	0.417172	−	0.417172i
$748$	137.445	+	7918.15i	0.00671857	+	0.387054i
$749$	10177.6	−	10177.6i	0.496503	−	0.496503i
$750$		−	21276.6i		−	1.03588i
$751$			5591.62i			0.271692i	0.990730	+	0.135846i	$0.0433753\pi$
$751$			5591.62i			0.271692i	−0.990730	+	0.135846i	$0.956625\pi$
$752$	31964.4	−	31964.4i	1.55003	−	1.55003i
$753$			29525.1i			1.42889i
$754$	12359.5	−	13882.9i	0.596957	−	0.670539i
$755$			93.3051i			0.00449764i
$756$	1817.71	−	1817.71i	0.0874464	−	0.0874464i
$757$	13484.9			0.647449			0.323724	−	0.946151i	$-0.395065\pi$
$757$	13484.9			0.647449			0.323724	+	0.946151i	$0.395065\pi$
$758$	33308.3			1.59606
$759$	−1006.15	−	57963.9i	−0.0481172	−	2.77201i
$760$	3384.57	+	3384.57i	0.161541	+	0.161541i
$761$	1628.07	+	1628.07i	0.0775525	+	0.0775525i	0.744819	−	0.667267i	$-0.232536\pi$
$761$	1628.07	+	1628.07i	0.0775525	+	0.0775525i	−0.667267	+	0.744819i	$0.732536\pi$
$762$	−468.979	+	468.979i	−0.0222957	+	0.0222957i
$763$	−2509.59			−0.119074
$764$		−	2411.20i		−	0.114181i
$765$	−3336.91	−	3336.91i	−0.157707	−	0.157707i
$766$	29042.6			1.36991
$767$	−8663.10	−	7712.46i	−0.407831	−	0.363078i
$768$	−39550.2			−1.85826
$769$	−1283.06	+	1283.06i	−0.0601669	+	0.0601669i	−0.736550	−	0.676383i	$-0.763546\pi$
$769$	−1283.06	+	1283.06i	−0.0601669	+	0.0601669i	0.676383	+	0.736550i	$0.263546\pi$
$770$	5821.79	+	5623.13i	0.272471	+	0.263173i
$771$		−	49020.9i		−	2.28981i
$772$	−1046.16	+	1046.16i	−0.0487720	+	0.0487720i
$773$	12891.8	+	12891.8i	0.599852	+	0.599852i	0.940273	−	0.340421i	$-0.110570\pi$
$773$	12891.8	+	12891.8i	0.599852	+	0.599852i	−0.340421	+	0.940273i	$0.610570\pi$
$774$	−28283.7	+	28283.7i	−1.31348	+	1.31348i
$775$	17441.8	−	17441.8i	0.808424	−	0.808424i
$776$			7252.74i			0.335513i
$777$	−55428.1			−2.55917
$778$	−19529.0	−	19529.0i	−0.899933	−	0.899933i
$779$			32334.4i			1.48716i
$780$	4079.33	+	3631.68i	0.187261	+	0.166712i
$781$	14454.8	+	13961.6i	0.662273	+	0.639673i
$782$	24485.5	+	24485.5i	1.11969	+	1.11969i
$783$			3240.70i			0.147910i
$784$			1329.12i			0.0605464i
$785$	5611.73	+	5611.73i	0.255148	+	0.255148i
$786$	−13768.7	−	13768.7i	−0.624828	−	0.624828i
$787$	−2986.54	−	2986.54i	−0.135271	−	0.135271i	0.636229	−	0.771500i	$-0.280493\pi$
$787$	−2986.54	−	2986.54i	−0.135271	−	0.135271i	−0.771500	+	0.636229i	$0.780493\pi$
$788$	990.686	+	990.686i	0.0447865	+	0.0447865i
$789$		−	6941.22i		−	0.313199i
$790$		−	6727.97i		−	0.303001i
$791$	−13489.4	−	13489.4i	−0.606354	−	0.606354i
$792$	−9609.57	−	9281.65i	−0.431138	−	0.416426i
$793$	31864.4	−	1849.82i	1.42691	−	0.0828360i
$794$			43617.2i			1.94952i
$795$	−2003.59	−	2003.59i	−0.0893839	−	0.0893839i
$796$	15052.9			0.670271
$797$		−	9909.36i		−	0.440411i	−0.975454	−	0.220205i	$-0.929327\pi$
$797$		−	9909.36i		−	0.440411i	0.975454	−	0.220205i	$-0.0706728\pi$
$798$	44470.5	−	44470.5i	1.97273	−	1.97273i
$799$	−18709.5	+	18709.5i	−0.828403	+	0.828403i
$800$	15185.2	+	15185.2i	0.671099	+	0.671099i
$801$	7122.20	−	7122.20i	0.314170	−	0.314170i
$802$			756.669i			0.0333154i
$803$	7987.24	+	7714.68i	0.351013	+	0.339035i
$804$	−1605.91	+	1605.91i	−0.0704429	+	0.0704429i
$805$	13029.2			0.570458
$806$	2087.92	+	35965.9i	0.0912453	+	1.57177i
$807$	43029.3			1.87696
$808$	−14077.5	−	14077.5i	−0.612928	−	0.612928i
$809$		−	35930.0i		−	1.56147i	−0.624860	−	0.780737i	$-0.714844\pi$
$809$		−	35930.0i		−	1.56147i	0.624860	−	0.780737i	$-0.285156\pi$
$810$	7148.81			0.310103
$811$	−14257.9	+	14257.9i	−0.617340	+	0.617340i	−0.944848	−	0.327508i	$-0.893791\pi$
$811$	−14257.9	+	14257.9i	−0.617340	+	0.617340i	0.327508	+	0.944848i	$0.393791\pi$
$812$	6966.58	+	6966.58i	0.301083	+	0.301083i
$813$	22286.1	+	22286.1i	0.961388	+	0.961388i
$814$	−865.901	−	49884.2i	−0.0372848	−	2.14796i
$815$	4825.70			0.207407
$816$	28175.4			1.20875
$817$	−31603.3	+	31603.3i	−1.35332	+	1.35332i
$818$			9709.76i			0.415029i
$819$	−18220.4	+	20466.3i	−0.777379	+	0.873199i
$820$		−	4042.96i		−	0.172178i
$821$	−27335.3	+	27335.3i	−1.16201	+	1.16201i	−0.177973	+	0.984035i	$0.556954\pi$
$821$	−27335.3	+	27335.3i	−1.16201	+	1.16201i	−0.984035	+	0.177973i	$0.943046\pi$
$822$			47495.0i			2.01530i
$823$			11966.0i			0.506817i	0.967359	+	0.253408i	$0.0815516\pi$
$823$			11966.0i			0.506817i	−0.967359	+	0.253408i	$0.918448\pi$
$824$	−1828.74	+	1828.74i	−0.0773144	+	0.0773144i
$825$	549.819	+	31674.9i	0.0232027	+	1.33670i
$826$	11808.4	−	11808.4i	0.497418	−	0.497418i
$827$	−23842.6	−	23842.6i	−1.00252	−	1.00252i	−0.999997	−	0.00252753i	$-0.999195\pi$
$827$	−23842.6	−	23842.6i	−1.00252	−	1.00252i	−0.00252753	−	0.999997i	$-0.500805\pi$
$828$	30023.6			1.26014
$829$		−	6892.31i		−	0.288757i	−0.989523	−	0.144379i	$-0.953882\pi$
$829$		−	6892.31i		−	0.288757i	0.989523	−	0.144379i	$-0.0461183\pi$
$830$	−3232.27	+	3232.27i	−0.135173	+	0.135173i
$831$	−31162.7			−1.30087
$832$	−1528.58	+	88.7380i	−0.0636945	+	0.00369764i
$833$		−	777.963i		−	0.0323587i
$834$	47481.6	+	47481.6i	1.97141	+	1.97141i
$835$		−	6805.04i		−	0.282034i
$836$	14989.9	+	14478.4i	0.620140	+	0.598978i
$837$	−4441.47	−	4441.47i	−0.183416	−	0.183416i
$838$	−8772.49	+	8772.49i	−0.361624	+	0.361624i
$839$	24426.4	−	24426.4i	1.00512	−	1.00512i	0.00512971	−	0.999987i	$-0.498367\pi$
$839$	24426.4	−	24426.4i	1.00512	−	1.00512i	0.999987	−	0.00512971i	$-0.00163284\pi$
$840$	3982.99	−	3982.99i	0.163602	−	0.163602i
$841$	11968.6			0.490739
$842$	14592.3			0.597251
$843$	−33400.7	−	33400.7i	−1.36463	−	1.36463i
$844$	14537.2			0.592882
$845$	−5663.82	−	4481.87i	−0.230582	−	0.182463i
$846$			62315.6i			2.53245i
$847$	−18458.7	−	17219.7i	−0.748816	−	0.698554i
$848$	9018.15			0.365194
$849$	9959.52			0.402603
$850$	−13380.3	−	13380.3i	−0.539929	−	0.539929i
$851$	−56789.5	−	56789.5i	−2.28757	−	2.28757i
$852$	−13805.9	+	13805.9i	−0.555143	+	0.555143i
$853$	20722.8	+	20722.8i	0.831813	+	0.831813i	0.987765	−	0.155952i	$-0.0498445\pi$
$853$	20722.8	+	20722.8i	0.831813	+	0.831813i	−0.155952	+	0.987765i	$0.549845\pi$
$854$			45954.9i			1.84139i
$855$	−12418.7			−0.496737
$856$	6375.34	−	6375.34i	0.254561	−	0.254561i
$857$	−33826.8			−1.34831			−0.674155	−	0.738590i	$-0.735492\pi$
$857$	−33826.8			−1.34831			−0.674155	+	0.738590i	$0.735492\pi$
$858$	−35087.4	−	30161.9i	−1.39611	−	1.20013i
$859$	21114.1			0.838654			0.419327	−	0.907835i	$-0.362266\pi$
$859$	21114.1			0.838654			0.419327	+	0.907835i	$0.362266\pi$
$860$	3951.56	−	3951.56i	0.156683	−	0.156683i
$861$	38051.3			1.50614
$862$			53950.3i			2.13174i
$863$	5606.32	+	5606.32i	0.221137	+	0.221137i	0.808977	−	0.587840i	$-0.200022\pi$
$863$	5606.32	+	5606.32i	0.221137	+	0.221137i	−0.587840	+	0.808977i	$0.700022\pi$
$864$	3866.84	−	3866.84i	0.152260	−	0.152260i
$865$	2760.15	+	2760.15i	0.108495	+	0.108495i
$866$	−18125.1	−	18125.1i	−0.711218	−	0.711218i
$867$	20867.7			0.817422
$868$	−19095.7			−0.746719
$869$	364.177	+	20980.1i	0.0142162	+	0.818988i
$870$		−	9913.39i		−	0.386316i
$871$	1997.03	−	2243.19i	0.0776886	−	0.0872646i
$872$	−1572.03			−0.0610501
$873$	−13305.9	−	13305.9i	−0.515849	−	0.515849i
$874$	91125.4			3.52673
$875$	−14913.7			−0.576199
$876$	−7628.64	+	7628.64i	−0.294233	+	0.294233i
$877$	27754.5	−	27754.5i	1.06865	−	1.06865i	0.0711847	−	0.997463i	$-0.477322\pi$
$877$	27754.5	−	27754.5i	1.06865	−	1.06865i	0.997463	−	0.0711847i	$-0.0226780\pi$
$878$	10761.6	−	10761.6i	0.413652	−	0.413652i
$879$	−2040.58	−	2040.58i	−0.0783016	−	0.0783016i
$880$	6863.68	+	6629.46i	0.262926	+	0.253953i
$881$		−	11723.2i		−	0.448313i	−0.974553	−	0.224156i	$-0.928037\pi$
$881$		−	11723.2i		−	0.448313i	0.974553	−	0.224156i	$-0.0719626\pi$
$882$	−1295.58	−	1295.58i	−0.0494607	−	0.0494607i
$883$			27691.8i			1.05538i	0.849436	+	0.527691i	$0.176942\pi$
$883$			27691.8i			1.05538i	−0.849436	+	0.527691i	$0.823058\pi$
$884$	10157.5	−	589.668i	0.386462	−	0.0224352i
$885$	−6186.07			−0.234963
$886$	−9562.00	+	9562.00i	−0.362575	+	0.362575i
$887$			568.747i			0.0215295i	0.999942	+	0.0107647i	$0.00342659\pi$
$887$			568.747i			0.0215295i	−0.999942	+	0.0107647i	$0.996573\pi$
$888$	−34720.8			−1.31211
$889$	328.727	+	328.727i	0.0124017	+	0.0124017i
$890$	−2702.87	+	2702.87i	−0.101798	+	0.101798i
$891$	−22292.4	+	386.956i	−0.838185	+	0.0145494i
$892$	−15323.2	+	15323.2i	−0.575179	+	0.575179i
$893$			69629.5i			2.60925i
$894$		−	33435.3i		−	1.25083i
$895$	3119.60	−	3119.60i	0.116510	−	0.116510i
$896$			26329.5i			0.981704i
$897$	−74356.5	+	4316.60i	−2.76777	+	0.160677i
$898$			30620.0i			1.13786i
$899$	17022.4	−	17022.4i	0.631513	−	0.631513i
$900$	−16406.7			−0.607654
$901$	−5278.53			−0.195176
$902$	594.439	+	34245.4i	0.0219431	+	1.26413i
$903$	37191.0	+	37191.0i	1.37059	+	1.37059i
$904$	−8449.88	−	8449.88i	−0.310883	−	0.310883i
$905$	6380.92	−	6380.92i	0.234374	−	0.234374i
$906$	767.949			0.0281605
$907$		−	20312.8i		−	0.743633i	−0.928306	−	0.371817i	$-0.878735\pi$
$907$		−	20312.8i		−	0.743633i	0.928306	−	0.371817i	$-0.121265\pi$
$908$	−3715.94	−	3715.94i	−0.135812	−	0.135812i
$909$	51653.3			1.88474
$910$	6914.65	−	7766.95i	0.251888	−	0.282936i
$911$	−7880.56			−0.286602			−0.143301	−	0.989679i	$-0.545772\pi$
$911$	−7880.56			−0.286602			−0.143301	+	0.989679i	$0.545772\pi$
$912$	52429.0	−	52429.0i	1.90362	−	1.90362i
$913$	9904.34	−	10254.3i	0.359021	−	0.371705i
$914$		−	53520.2i		−	1.93686i
$915$	12037.2	−	12037.2i	0.434903	−	0.434903i
$916$	−15565.7	−	15565.7i	−0.561467	−	0.561467i
$917$	−9651.11	+	9651.11i	−0.347555	+	0.347555i
$918$	−3407.22	+	3407.22i	−0.122500	+	0.122500i
$919$			13298.5i			0.477343i	0.971100	+	0.238671i	$0.0767119\pi$
$919$			13298.5i			0.477343i	−0.971100	+	0.238671i	$0.923288\pi$
$920$	8161.62			0.292479
$921$	−25359.4	−	25359.4i	−0.907296	−	0.907296i
$922$			50374.9i			1.79936i
$923$	17168.3	−	19284.5i	0.612244	−	0.687710i
$924$	17038.3	−	17640.2i	0.606621	−	0.628053i
$925$	31033.1	+	31033.1i	1.10309	+	1.10309i
$926$		−	24590.3i		−	0.872665i
$927$		−	6710.01i		−	0.237741i
$928$	14820.1	+	14820.1i	0.524240	+	0.524240i
$929$	−9217.91	−	9217.91i	−0.325543	−	0.325543i	0.525346	−	0.850889i	$-0.323936\pi$
$929$	−9217.91	−	9217.91i	−0.325543	−	0.325543i	−0.850889	+	0.525346i	$0.823936\pi$
$930$	13586.5	+	13586.5i	0.479054	+	0.479054i
$931$	−1447.64	−	1447.64i	−0.0509607	−	0.0509607i
$932$		−	16806.6i		−	0.590686i
$933$		−	22495.3i		−	0.789351i
$934$	−6623.35	−	6623.35i	−0.232037	−	0.232037i
$935$	−4017.47	−	3880.38i	−0.140519	−	0.135724i
$936$	−11413.5	+	12820.3i	−0.398569	+	0.447697i
$937$		−	29422.0i		−	1.02580i	−0.858449	−	0.512900i	$-0.828571\pi$
$937$		−	29422.0i		−	1.02580i	0.858449	−	0.512900i	$-0.171429\pi$
$938$	3057.62	+	3057.62i	0.106434	+	0.106434i
$939$	−9122.37			−0.317036
$940$		−	8706.20i		−	0.302090i
$941$	5892.29	−	5892.29i	0.204127	−	0.204127i	−0.597639	−	0.801765i	$-0.703894\pi$
$941$	5892.29	−	5892.29i	0.204127	−	0.204127i	0.801765	+	0.597639i	$0.203894\pi$
$942$	46187.4	−	46187.4i	1.59752	−	1.59752i
$943$	38985.9	+	38985.9i	1.34629	+	1.34629i
$944$	13921.7	−	13921.7i	0.479992	−	0.479992i
$945$			1813.05i			0.0624111i
$946$	−32890.2	+	34052.2i	−1.13039	+	1.17033i
$947$	−18785.3	+	18785.3i	−0.644603	+	0.644603i	−0.951684	−	0.307081i	$-0.900648\pi$
$947$	−18785.3	+	18785.3i	−0.644603	+	0.644603i	0.307081	+	0.951684i	$0.400648\pi$
$948$	−20386.0			−0.698424
$949$	9486.59	−	10655.9i	0.324497	−	0.364495i
$950$	−49796.2			−1.70063
$951$	−40217.0	−	40217.0i	−1.37132	−	1.37132i
$952$		−	10493.3i		−	0.357237i
$953$	6023.75			0.204752			0.102376	−	0.994746i	$-0.467356\pi$
$953$	6023.75			0.204752			0.102376	+	0.994746i	$0.467356\pi$
$954$	−8790.58	+	8790.58i	−0.298329	+	0.298329i
$955$	1202.51	+	1202.51i	0.0407458	+	0.0407458i
$956$	3738.43	+	3738.43i	0.126474	+	0.126474i
$957$	536.599	+	30913.3i	0.0181252	+	1.04418i
$958$	−43617.6			−1.47100
$959$	33291.3			1.12099
$960$	−577.438	+	577.438i	−0.0194133	+	0.0194133i
$961$			16868.3i			0.566222i
$962$	−63991.7	+	3714.89i	−2.14467	+	0.124504i
$963$			23392.4i			0.782772i
$964$	−19142.7	+	19142.7i	−0.639569	+	0.639569i
$965$		−	1043.47i		−	0.0348089i
$966$		−	107237.i		−	3.57173i
$967$	1350.28	−	1350.28i	0.0449038	−	0.0449038i	−0.684298	−	0.729202i	$-0.739891\pi$
$967$	1350.28	−	1350.28i	0.0449038	−	0.0449038i	0.729202	+	0.684298i	$0.239891\pi$
$968$	−11562.7	−	10786.6i	−0.383925	−	0.358155i
$969$	−30687.9	+	30687.9i	−1.01738	+	1.01738i
$970$	5049.58	+	5049.58i	0.167147	+	0.167147i
$971$	15875.2			0.524676			0.262338	−	0.964976i	$-0.415506\pi$
$971$	15875.2			0.524676			0.262338	+	0.964976i	$0.415506\pi$
$972$		−	25320.7i		−	0.835557i
$973$	33281.9	−	33281.9i	1.09658	−	1.09658i
$974$	5186.88			0.170635
$975$	40632.7	−	2358.84i	1.33465	−	0.0774804i
$976$			54179.1i			1.77688i
$977$	−5422.72	−	5422.72i	−0.177572	−	0.177572i	0.612724	−	0.790297i	$-0.290074\pi$
$977$	−5422.72	−	5422.72i	−0.177572	−	0.177572i	−0.790297	+	0.612724i	$0.790074\pi$
$978$		−	39718.0i		−	1.29861i
$979$	8282.17	−	8574.77i	0.270377	−	0.279929i
$980$	181.007	+	181.007i	0.00590006	+	0.00590006i
$981$	2884.05	−	2884.05i	0.0938640	−	0.0938640i
$982$	−22086.3	+	22086.3i	−0.717721	+	0.717721i
$983$	−445.004	+	445.004i	−0.0144389	+	0.0144389i	−0.714289	−	0.699850i	$-0.753250\pi$
$983$	−445.004	+	445.004i	−0.0144389	+	0.0144389i	0.699850	+	0.714289i	$0.253250\pi$
$984$	23835.7			0.772210
$985$	−988.146			−0.0319644
$986$	−13058.6	−	13058.6i	−0.421774	−	0.421774i
$987$	81940.4			2.64255
$988$	17803.8	−	19998.3i	0.573293	−	0.643958i
$989$			76208.9i			2.45025i
$990$	−13152.7	+	228.307i	−0.422241	+	0.00732935i
$991$	−33262.2			−1.06621			−0.533103	−	0.846051i	$-0.678974\pi$
$991$	−33262.2			−1.06621			−0.533103	+	0.846051i	$0.678974\pi$
$992$	−40622.7			−1.30017
$993$	−9893.15	−	9893.15i	−0.316163	−	0.316163i
$994$	26286.1	+	26286.1i	0.838777	+	0.838777i
$995$	−7507.14	+	7507.14i	−0.239188	+	0.239188i
$996$	9793.88	+	9793.88i	0.311577	+	0.311577i
$997$			16174.4i			0.513789i	0.966440	+	0.256894i	$0.0826992\pi$
$997$			16174.4i			0.513789i	−0.966440	+	0.256894i	$0.917301\pi$
$998$	−20337.9			−0.645075
$999$	7902.41	−	7902.41i	0.250272	−	0.250272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.9	✓	80
11.10	odd	2	inner	143.4.g.a.21.32	yes	80
13.5	odd	4	inner	143.4.g.a.109.32	yes	80
143.109	even	4	inner	143.4.g.a.109.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.9	✓	80	1.1	even	1	trivial
143.4.g.a.21.32	yes	80	11.10	odd	2	inner
143.4.g.a.109.9	yes	80	143.109	even	4	inner
143.4.g.a.109.32	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)

\(f(q)\)	\(=\)	\(q+(-2.51606 + 2.51606i) q^{2} -7.60421 q^{3} -4.66116i q^{4} +(2.32460 + 2.32460i) q^{5} +(19.1327 - 19.1327i) q^{6} +(-13.4109 - 13.4109i) q^{7} +(-8.40074 - 8.40074i) q^{8} +30.8240 q^{9} +O(q^{10})\)	\(q+(-2.51606 + 2.51606i) q^{2} -7.60421 q^{3} -4.66116i q^{4} +(2.32460 + 2.32460i) q^{5} +(19.1327 - 19.1327i) q^{6} +(-13.4109 - 13.4109i) q^{7} +(-8.40074 - 8.40074i) q^{8} +30.8240 q^{9} -11.6977 q^{10} +(36.4774 - 0.633182i) q^{11} +35.4444i q^{12} +(-2.71648 - 46.7934i) q^{13} +67.4854 q^{14} +(-17.6768 - 17.6768i) q^{15} +79.5629 q^{16} -46.5700 q^{17} +(-77.5552 + 77.5552i) q^{18} +(-86.6577 + 86.6577i) q^{19} +(10.8353 - 10.8353i) q^{20} +(101.979 + 101.979i) q^{21} +(-90.1863 + 93.3726i) q^{22} +208.968i q^{23} +(63.8810 + 63.8810i) q^{24} -114.192i q^{25} +(124.570 + 110.900i) q^{26} -29.0785 q^{27} +(-62.5104 + 62.5104i) q^{28} -111.447i q^{29} +88.9518 q^{30} +(152.741 + 152.741i) q^{31} +(-132.979 + 132.979i) q^{32} +(-277.382 + 4.81485i) q^{33} +(117.173 - 117.173i) q^{34} -62.3501i q^{35} -143.676i q^{36} +(-271.761 + 271.761i) q^{37} -436.073i q^{38} +(20.6567 + 355.827i) q^{39} -39.0568i q^{40} +(186.564 - 186.564i) q^{41} -513.173 q^{42} +364.691 q^{43} +(-2.95136 - 170.027i) q^{44} +(71.6536 + 71.6536i) q^{45} +(-525.777 - 525.777i) q^{46} +(401.750 - 401.750i) q^{47} -605.013 q^{48} +16.7052i q^{49} +(287.316 + 287.316i) q^{50} +354.128 q^{51} +(-218.111 + 12.6620i) q^{52} +113.346 q^{53} +(73.1634 - 73.1634i) q^{54} +(86.2673 + 83.3235i) q^{55} +225.323i q^{56} +(658.964 - 658.964i) q^{57} +(280.407 + 280.407i) q^{58} +(174.977 - 174.977i) q^{59} +(-82.3943 + 82.3943i) q^{60} +680.960i q^{61} -768.610 q^{62} +(-413.378 - 413.378i) q^{63} -32.6665i q^{64} +(102.461 - 115.091i) q^{65} +(685.796 - 710.024i) q^{66} +(45.3079 + 45.3079i) q^{67} +217.070i q^{68} -1589.04i q^{69} +(156.877 + 156.877i) q^{70} +(389.508 + 389.508i) q^{71} +(-258.944 - 258.944i) q^{72} +(215.228 + 215.228i) q^{73} -1367.54i q^{74} +868.343i q^{75} +(403.926 + 403.926i) q^{76} +(-497.687 - 480.703i) q^{77} +(-947.256 - 843.309i) q^{78} +575.153i q^{79} +(184.952 + 184.952i) q^{80} -611.129 q^{81} +938.812i q^{82} +(276.317 - 276.317i) q^{83} +(475.342 - 475.342i) q^{84} +(-108.257 - 108.257i) q^{85} +(-917.587 + 917.587i) q^{86} +847.464i q^{87} +(-311.756 - 301.118i) q^{88} +(231.060 - 231.060i) q^{89} -360.570 q^{90} +(-591.112 + 663.973i) q^{91} +974.034 q^{92} +(-1161.47 - 1161.47i) q^{93} +2021.66i q^{94} -402.890 q^{95} +(1011.20 - 1011.20i) q^{96} +(-431.673 - 431.673i) q^{97} +(-42.0314 - 42.0314i) q^{98} +(1124.38 - 19.5172i) 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

Fields

Representations

Groups

Database

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