LMFDB - Embedded newform 143.4.g.a.21.13

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			21.13
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74793 + 1.74793i) q^{2} -3.12343 q^{3} +1.88950i q^{4} +(-2.44120 - 2.44120i) q^{5} +(5.45953 - 5.45953i) q^{6} +(8.07208 + 8.07208i) q^{7} +(-17.2861 - 17.2861i) q^{8} -17.2442 q^{9} +O(q^{10})$	\(q+(-1.74793 + 1.74793i) q^{2} -3.12343 q^{3} +1.88950i q^{4} +(-2.44120 - 2.44120i) q^{5} +(5.45953 - 5.45953i) q^{6} +(8.07208 + 8.07208i) q^{7} +(-17.2861 - 17.2861i) q^{8} -17.2442 q^{9} +8.53410 q^{10} +(-22.1285 + 29.0057i) q^{11} -5.90172i q^{12} +(-2.33233 - 46.8141i) q^{13} -28.2188 q^{14} +(7.62493 + 7.62493i) q^{15} +45.3138 q^{16} +37.3690 q^{17} +(30.1416 - 30.1416i) q^{18} +(90.0989 - 90.0989i) q^{19} +(4.61266 - 4.61266i) q^{20} +(-25.2126 - 25.2126i) q^{21} +(-12.0208 - 89.3788i) q^{22} +24.8687i q^{23} +(53.9920 + 53.9920i) q^{24} -113.081i q^{25} +(85.9044 + 77.7509i) q^{26} +138.194 q^{27} +(-15.2522 + 15.2522i) q^{28} -77.2710i q^{29} -26.6556 q^{30} +(-60.5432 - 60.5432i) q^{31} +(59.0838 - 59.0838i) q^{32} +(69.1168 - 90.5971i) q^{33} +(-65.3184 + 65.3184i) q^{34} -39.4112i q^{35} -32.5829i q^{36} +(50.1076 - 50.1076i) q^{37} +314.973i q^{38} +(7.28486 + 146.221i) q^{39} +84.3980i q^{40} +(-83.3477 + 83.3477i) q^{41} +88.1394 q^{42} -102.476 q^{43} +(-54.8062 - 41.8118i) q^{44} +(42.0966 + 42.0966i) q^{45} +(-43.4687 - 43.4687i) q^{46} +(270.808 - 270.808i) q^{47} -141.534 q^{48} -212.683i q^{49} +(197.657 + 197.657i) q^{50} -116.720 q^{51} +(88.4552 - 4.40693i) q^{52} -691.201 q^{53} +(-241.552 + 241.552i) q^{54} +(124.829 - 16.7885i) q^{55} -279.070i q^{56} +(-281.417 + 281.417i) q^{57} +(135.064 + 135.064i) q^{58} +(-480.647 + 480.647i) q^{59} +(-14.4073 + 14.4073i) q^{60} +126.405i q^{61} +211.650 q^{62} +(-139.196 - 139.196i) q^{63} +569.059i q^{64} +(-108.589 + 119.977i) q^{65} +(37.5460 + 279.168i) q^{66} +(96.5465 + 96.5465i) q^{67} +70.6088i q^{68} -77.6756i q^{69} +(68.8879 + 68.8879i) q^{70} +(-567.646 - 567.646i) q^{71} +(298.085 + 298.085i) q^{72} +(-498.050 - 498.050i) q^{73} +175.169i q^{74} +353.201i q^{75} +(170.242 + 170.242i) q^{76} +(-412.759 + 55.5129i) q^{77} +(-268.316 - 242.849i) q^{78} -882.786i q^{79} +(-110.620 - 110.620i) q^{80} +33.9555 q^{81} -291.371i q^{82} +(-454.739 + 454.739i) q^{83} +(47.6391 - 47.6391i) q^{84} +(-91.2255 - 91.2255i) q^{85} +(179.120 - 179.120i) q^{86} +241.350i q^{87} +(883.912 - 118.879i) q^{88} +(524.025 - 524.025i) q^{89} -147.164 q^{90} +(359.060 - 396.714i) q^{91} -46.9894 q^{92} +(189.102 + 189.102i) q^{93} +946.706i q^{94} -439.900 q^{95} +(-184.544 + 184.544i) q^{96} +(1064.54 + 1064.54i) q^{97} +(371.755 + 371.755i) q^{98} +(381.588 - 500.179i) 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 $

$2$	−1.74793	+	1.74793i	−0.617986	+	0.617986i	−0.945014	−	0.327029i	$-0.893953\pi$
$2$	−1.74793	+	1.74793i	−0.617986	+	0.617986i	0.327029	+	0.945014i	$0.393953\pi$
$3$	−3.12343			−0.601104			−0.300552	−	0.953765i	$-0.597171\pi$
$3$	−3.12343			−0.601104			−0.300552	+	0.953765i	$0.597171\pi$
$4$			1.88950i			0.236187i
$5$	−2.44120	−	2.44120i	−0.218348	−	0.218348i	0.589454	−	0.807802i	$-0.299343\pi$
$5$	−2.44120	−	2.44120i	−0.218348	−	0.218348i	−0.807802	+	0.589454i	$0.799343\pi$
$6$	5.45953	−	5.45953i	0.371474	−	0.371474i
$7$	8.07208	+	8.07208i	0.435851	+	0.435851i	0.890613	−	0.454762i	$-0.150276\pi$
$7$	8.07208	+	8.07208i	0.435851	+	0.435851i	−0.454762	+	0.890613i	$0.650276\pi$
$8$	−17.2861	−	17.2861i	−0.763946	−	0.763946i
$9$	−17.2442			−0.638674
$10$	8.53410			0.269872
$11$	−22.1285	+	29.0057i	−0.606545	+	0.795049i
$11$	−22.1285	+	29.0057i	−0.606545	+	0.795049i
$12$		−	5.90172i		−	0.141973i
$13$	−2.33233	−	46.8141i	−0.0497593	−	0.998761i
$13$	−2.33233	−	46.8141i	−0.0497593	−	0.998761i
$14$	−28.2188			−0.538700
$15$	7.62493	+	7.62493i	0.131250	+	0.131250i
$16$	45.3138			0.708028
$17$	37.3690			0.533137			0.266568	−	0.963816i	$-0.414110\pi$
$17$	37.3690			0.533137			0.266568	+	0.963816i	$0.414110\pi$
$18$	30.1416	−	30.1416i	0.394691	−	0.394691i
$19$	90.0989	−	90.0989i	1.08790	−	1.08790i	0.0921553	−	0.995745i	$-0.470624\pi$
$19$	90.0989	−	90.0989i	1.08790	−	1.08790i	0.995745	−	0.0921553i	$-0.0293756\pi$
$20$	4.61266	−	4.61266i	0.0515711	−	0.0515711i
$21$	−25.2126	−	25.2126i	−0.261992	−	0.261992i
$22$	−12.0208	−	89.3788i	−0.116493	−	0.866165i
$23$			24.8687i			0.225456i	0.993626	+	0.112728i	$0.0359588\pi$
$23$			24.8687i			0.225456i	−0.993626	+	0.112728i	$0.964041\pi$
$24$	53.9920	+	53.9920i	0.459211	+	0.459211i
$25$		−	113.081i		−	0.904648i
$26$	85.9044	+	77.7509i	0.647971	+	0.586470i
$27$	138.194			0.985014
$28$	−15.2522	+	15.2522i	−0.102943	+	0.102943i
$29$		−	77.2710i		−	0.494788i	−0.968915	−	0.247394i	$-0.920426\pi$
$29$		−	77.2710i		−	0.494788i	0.968915	−	0.247394i	$-0.0795743\pi$
$30$	−26.6556			−0.162221
$31$	−60.5432	−	60.5432i	−0.350770	−	0.350770i	0.509626	−	0.860396i	$-0.329784\pi$
$31$	−60.5432	−	60.5432i	−0.350770	−	0.350770i	−0.860396	+	0.509626i	$0.829784\pi$
$32$	59.0838	−	59.0838i	0.326395	−	0.326395i
$33$	69.1168	−	90.5971i	0.364597	−	0.477907i
$34$	−65.3184	+	65.3184i	−0.329471	+	0.329471i
$35$		−	39.4112i		−	0.190334i
$36$		−	32.5829i		−	0.150847i
$37$	50.1076	−	50.1076i	0.222639	−	0.222639i	−0.586970	−	0.809609i	$-0.699679\pi$
$37$	50.1076	−	50.1076i	0.222639	−	0.222639i	0.809609	+	0.586970i	$0.199679\pi$
$38$			314.973i			1.34461i
$39$	7.28486	+	146.221i	0.0299105	+	0.600359i
$40$			84.3980i			0.333612i
$41$	−83.3477	+	83.3477i	−0.317481	+	0.317481i	−0.847799	−	0.530318i	$-0.822073\pi$
$41$	−83.3477	+	83.3477i	−0.317481	+	0.317481i	0.530318	+	0.847799i	$0.322073\pi$
$42$	88.1394			0.323815
$43$	−102.476			−0.363427			−0.181714	−	0.983351i	$-0.558164\pi$
$43$	−102.476			−0.363427			−0.181714	+	0.983351i	$0.558164\pi$
$44$	−54.8062	−	41.8118i	−0.187781	−	0.143258i
$45$	42.0966	+	42.0966i	0.139453	+	0.139453i
$46$	−43.4687	−	43.4687i	−0.139328	−	0.139328i
$47$	270.808	−	270.808i	0.840456	−	0.840456i	−0.148462	−	0.988918i	$-0.547432\pi$
$47$	270.808	−	270.808i	0.840456	−	0.840456i	0.988918	+	0.148462i	$0.0474323\pi$
$48$	−141.534			−0.425599
$49$		−	212.683i		−	0.620067i
$50$	197.657	+	197.657i	0.559060	+	0.559060i
$51$	−116.720			−0.320471
$52$	88.4552	−	4.40693i	0.235895	−	0.0117525i
$53$	−691.201			−1.79139			−0.895695	−	0.444668i	$-0.853322\pi$
$53$	−691.201			−1.79139			−0.895695	+	0.444668i	$0.853322\pi$
$54$	−241.552	+	241.552i	−0.608724	+	0.608724i
$55$	124.829	−	16.7885i	0.306035	−	0.0411594i
$56$		−	279.070i		−	0.665934i
$57$	−281.417	+	281.417i	−0.653941	+	0.653941i
$58$	135.064	+	135.064i	0.305772	+	0.305772i
$59$	−480.647	+	480.647i	−1.06059	+	1.06059i	−0.0625499	+	0.998042i	$0.519923\pi$
$59$	−480.647	+	480.647i	−1.06059	+	1.06059i	−0.998042	+	0.0625499i	$0.980077\pi$
$60$	−14.4073	+	14.4073i	−0.0309996	+	0.0309996i
$61$			126.405i			0.265320i	0.991162	+	0.132660i	$0.0423519\pi$
$61$			126.405i			0.265320i	−0.991162	+	0.132660i	$0.957648\pi$
$62$	211.650			0.433542
$63$	−139.196	−	139.196i	−0.278367	−	0.278367i
$64$			569.059i			1.11144i
$65$	−108.589	+	119.977i	−0.207213	+	0.228942i
$66$	37.5460	+	279.168i	0.0700241	+	0.520655i
$67$	96.5465	+	96.5465i	0.176045	+	0.176045i	0.789629	−	0.613584i	$-0.210273\pi$
$67$	96.5465	+	96.5465i	0.176045	+	0.176045i	−0.613584	+	0.789629i	$0.710273\pi$
$68$			70.6088i			0.125920i
$69$		−	77.6756i		−	0.135522i
$70$	68.8879	+	68.8879i	0.117624	+	0.117624i
$71$	−567.646	−	567.646i	−0.948833	−	0.948833i	0.0499204	−	0.998753i	$-0.484103\pi$
$71$	−567.646	−	567.646i	−0.948833	−	0.948833i	−0.998753	+	0.0499204i	$0.984103\pi$
$72$	298.085	+	298.085i	0.487912	+	0.487912i
$73$	−498.050	−	498.050i	−0.798525	−	0.798525i	0.184338	−	0.982863i	$-0.440986\pi$
$73$	−498.050	−	498.050i	−0.798525	−	0.798525i	−0.982863	+	0.184338i	$0.940986\pi$
$74$			175.169i			0.275175i
$75$			353.201i			0.543788i
$76$	170.242	+	170.242i	0.256948	+	0.256948i
$77$	−412.759	+	55.5129i	−0.610887	+	0.0821595i
$78$	−268.316	−	242.849i	−0.389498	−	0.352529i
$79$		−	882.786i		−	1.25723i	−0.777717	−	0.628615i	$-0.783622\pi$
$79$		−	882.786i		−	1.25723i	0.777717	−	0.628615i	$-0.216378\pi$
$80$	−110.620	−	110.620i	−0.154596	−	0.154596i
$81$	33.9555			0.0465782
$82$		−	291.371i		−	0.392397i
$83$	−454.739	+	454.739i	−0.601374	+	0.601374i	−0.940677	−	0.339303i	$-0.889809\pi$
$83$	−454.739	+	454.739i	−0.601374	+	0.601374i	0.339303	+	0.940677i	$0.389809\pi$
$84$	47.6391	−	47.6391i	0.0618792	−	0.0618792i
$85$	−91.2255	−	91.2255i	−0.116409	−	0.116409i
$86$	179.120	−	179.120i	0.224593	−	0.224593i
$87$			241.350i			0.297419i
$88$	883.912	−	118.879i	1.07074	−	0.144007i
$89$	524.025	−	524.025i	0.624119	−	0.624119i	−0.322463	−	0.946582i	$-0.604511\pi$
$89$	524.025	−	524.025i	0.624119	−	0.624119i	0.946582	+	0.322463i	$0.104511\pi$
$90$	−147.164			−0.172360
$91$	359.060	−	396.714i	0.413624	−	0.456999i
$92$	−46.9894			−0.0532498
$93$	189.102	+	189.102i	0.210849	+	0.210849i
$94$			946.706i			1.03878i
$95$	−439.900			−0.475082
$96$	−184.544	+	184.544i	−0.196197	+	0.196197i
$97$	1064.54	+	1064.54i	1.11431	+	1.11431i	0.992561	+	0.121745i	$0.0388489\pi$
$97$	1064.54	+	1064.54i	1.11431	+	1.11431i	0.121745	+	0.992561i	$0.461151\pi$
$98$	371.755	+	371.755i	0.383193	+	0.383193i
$99$	381.588	−	500.179i	0.387385	−	0.507777i
$100$	213.667			0.213667
$101$	95.5325			0.0941172			0.0470586	−	0.998892i	$-0.485015\pi$
$101$	95.5325			0.0941172			0.0470586	+	0.998892i	$0.485015\pi$
$102$	204.017	−	204.017i	0.198046	−	0.198046i
$103$			586.962i			0.561505i	0.959780	+	0.280753i	$0.0905841\pi$
$103$			586.962i			0.561505i	−0.959780	+	0.280753i	$0.909416\pi$
$104$	−768.918	+	849.551i	−0.724986	+	0.801013i
$105$			123.098i			0.114411i
$106$	1208.17	−	1208.17i	1.10705	−	1.10705i
$107$		−	1495.55i		−	1.35121i	−0.737262	−	0.675607i	$-0.763882\pi$
$107$		−	1495.55i		−	1.35121i	0.737262	−	0.675607i	$-0.236118\pi$
$108$			261.117i			0.232648i
$109$	−312.397	+	312.397i	−0.274516	+	0.274516i	−0.830915	−	0.556399i	$-0.812183\pi$
$109$	−312.397	+	312.397i	−0.274516	+	0.274516i	0.556399	+	0.830915i	$0.312183\pi$
$110$	−188.847	+	247.537i	−0.163690	+	0.214561i
$111$	−156.508	+	156.508i	−0.133829	+	0.133829i
$112$	365.776	+	365.776i	0.308595	+	0.308595i
$113$	−26.1458			−0.0217663			−0.0108831	−	0.999941i	$-0.503464\pi$
$113$	−26.1458			−0.0217663			−0.0108831	+	0.999941i	$0.503464\pi$
$114$		−	983.794i		−	0.808252i
$115$	60.7096	−	60.7096i	0.0492278	−	0.0492278i
$116$	146.004			0.116863
$117$	40.2191	+	807.272i	0.0317800	+	0.637883i
$118$		−	1680.27i		−	1.31086i
$119$	301.646	+	301.646i	0.232368	+	0.232368i
$120$		−	263.611i		−	0.200536i
$121$	−351.658	−	1283.70i	−0.264206	−	0.964466i
$122$	−220.947	−	220.947i	−0.163964	−	0.163964i
$123$	260.330	−	260.330i	0.190839	−	0.190839i
$124$	114.396	−	114.396i	0.0828475	−	0.0828475i
$125$	−581.205	+	581.205i	−0.415876	+	0.415876i
$126$	486.611			0.344053
$127$	1965.85			1.37355			0.686774	−	0.726871i	$-0.259026\pi$
$127$	1965.85			1.37355			0.686774	+	0.726871i	$0.259026\pi$
$128$	−522.003	−	522.003i	−0.360461	−	0.360461i
$129$	320.075			0.218458
$130$	−19.9043	−	399.516i	−0.0134286	−	0.269538i
$131$		−	2253.33i		−	1.50286i	−0.659814	−	0.751429i	$-0.729365\pi$
$131$		−	2253.33i		−	1.50286i	0.659814	−	0.751429i	$-0.270635\pi$
$132$	171.183	+	130.596i	0.112876	+	0.0861132i
$133$	1454.57			0.948325
$134$	−337.512			−0.217587
$135$	−337.359	−	337.359i	−0.215076	−	0.215076i
$136$	−645.966	−	645.966i	−0.407288	−	0.407288i
$137$	−1330.52	+	1330.52i	−0.829735	+	0.829735i	−0.987480	−	0.157745i	$-0.949578\pi$
$137$	−1330.52	+	1330.52i	−0.829735	+	0.829735i	0.157745	+	0.987480i	$0.449578\pi$
$138$	135.771	+	135.771i	0.0837508	+	0.0837508i
$139$		−	3133.50i		−	1.91209i	−0.293222	−	0.956044i	$-0.594728\pi$
$139$		−	3133.50i		−	1.91209i	0.293222	−	0.956044i	$-0.405272\pi$
$140$	74.4674			0.0449546
$141$	−845.850	+	845.850i	−0.505202	+	0.505202i
$142$	1984.41			1.17273
$143$	1409.49	+	968.276i	0.824245	+	0.566233i
$144$	−781.400			−0.452199
$145$	−188.634	+	188.634i	−0.108036	+	0.108036i
$146$	1741.11			0.986954
$147$			664.301i			0.372725i
$148$	94.6784	+	94.6784i	0.0525846	+	0.0525846i
$149$	−986.143	+	986.143i	−0.542201	+	0.542201i	−0.924174	−	0.381973i	$-0.875245\pi$
$149$	−986.143	+	986.143i	−0.542201	+	0.542201i	0.381973	+	0.924174i	$0.375245\pi$
$150$	−617.369	−	617.369i	−0.336053	−	0.336053i
$151$	−1174.83	−	1174.83i	−0.633155	−	0.633155i	0.315703	−	0.948858i	$-0.397760\pi$
$151$	−1174.83	−	1174.83i	−0.633155	−	0.633155i	−0.948858	+	0.315703i	$0.897760\pi$
$152$	−3114.92			−1.66219
$153$	−644.399			−0.340501
$154$	624.440	−	818.505i	0.326746	−	0.428293i
$155$			295.597i			0.153180i
$156$	−276.284	+	13.7647i	−0.141797	+	0.00706449i
$157$	−1415.96			−0.719781			−0.359890	−	0.932995i	$-0.617186\pi$
$157$	−1415.96			−0.719781			−0.359890	+	0.932995i	$0.617186\pi$
$158$	1543.04	+	1543.04i	0.776950	+	0.776950i
$159$	2158.92			1.07681
$160$	−288.471			−0.142535
$161$	−200.742	+	200.742i	−0.0982651	+	0.0982651i
$162$	−59.3517	+	59.3517i	−0.0287847	+	0.0287847i
$163$	−1495.52	+	1495.52i	−0.718638	+	0.718638i	−0.968326	−	0.249688i	$-0.919672\pi$
$163$	−1495.52	+	1495.52i	−0.718638	+	0.718638i	0.249688	+	0.968326i	$0.419672\pi$
$164$	−157.485	−	157.485i	−0.0749850	−	0.0749850i
$165$	−389.895	+	52.4378i	−0.183959	+	0.0247411i
$166$		−	1589.70i		−	0.743281i
$167$	2752.27	+	2752.27i	1.27531	+	1.27531i	0.943262	+	0.332049i	$0.107740\pi$
$167$	2752.27	+	2752.27i	1.27531	+	1.27531i	0.332049	+	0.943262i	$0.392260\pi$
$168$			871.655i			0.400295i
$169$	−2186.12	+	218.372i	−0.995048	+	0.0993954i
$170$	318.911			0.143879
$171$	−1553.68	+	1553.68i	−0.694813	+	0.694813i
$172$		−	193.628i		−	0.0858370i
$173$	−966.255			−0.424641			−0.212321	−	0.977200i	$-0.568102\pi$
$173$	−966.255			−0.424641			−0.212321	+	0.977200i	$0.568102\pi$
$174$	−421.863	−	421.863i	−0.183801	−	0.183801i
$175$	912.799	−	912.799i	0.394292	−	0.394292i
$176$	−1002.73	+	1314.36i	−0.429451	+	0.562917i
$177$	1501.27	−	1501.27i	0.637526	−	0.637526i
$178$			1831.92i			0.771393i
$179$		−	3249.03i		−	1.35667i	−0.734753	−	0.678335i	$-0.762702\pi$
$179$		−	3249.03i		−	1.35667i	0.734753	−	0.678335i	$-0.237298\pi$
$180$	−79.5415	+	79.5415i	−0.0329371	+	0.0329371i
$181$		−	426.216i		−	0.175030i	−0.996163	−	0.0875148i	$-0.972107\pi$
$181$		−	426.216i		−	0.175030i	0.996163	−	0.0875148i	$-0.0278925\pi$
$182$	65.8155	+	1321.04i	0.0268053	+	0.538032i
$183$		−	394.818i		−	0.159485i
$184$	429.883	−	429.883i	0.172236	−	0.172236i
$185$	−244.646			−0.0972256
$186$	−661.074			−0.260604
$187$	−826.922	+	1083.91i	−0.323372	+	0.423870i
$188$	511.692	+	511.692i	0.198505	+	0.198505i
$189$	1115.51	+	1115.51i	0.429319	+	0.429319i
$190$	768.913	−	768.913i	0.293594	−	0.293594i
$191$	965.228			0.365662			0.182831	−	0.983144i	$-0.441474\pi$
$191$	965.228			0.365662			0.182831	+	0.983144i	$0.441474\pi$
$192$		−	1777.41i		−	0.668093i
$193$	1142.07	+	1142.07i	0.425950	+	0.425950i	0.887246	−	0.461296i	$-0.152616\pi$
$193$	1142.07	+	1142.07i	0.425950	+	0.425950i	−0.461296	+	0.887246i	$0.652616\pi$
$194$	−3721.48			−1.37725
$195$	339.170	−	374.738i	0.124556	−	0.137618i
$196$	401.865			0.146452
$197$	−2877.50	+	2877.50i	−1.04068	+	1.04068i	−0.0415397	+	0.999137i	$0.513226\pi$
$197$	−2877.50	+	2877.50i	−1.04068	+	1.04068i	−0.999137	+	0.0415397i	$0.986774\pi$
$198$	207.288	+	1541.27i	0.0744007	+	0.553197i
$199$			2507.83i			0.893344i	0.894698	+	0.446672i	$0.147391\pi$
$199$			2507.83i			0.893344i	−0.894698	+	0.446672i	$0.852609\pi$
$200$	−1954.73	+	1954.73i	−0.691103	+	0.691103i
$201$	−301.556	−	301.556i	−0.105821	−	0.105821i
$202$	−166.984	+	166.984i	−0.0581631	+	0.0581631i
$203$	623.737	−	623.737i	0.215654	−	0.215654i
$204$		−	220.542i		−	0.0756912i
$205$	406.937			0.138643
$206$	−1025.97	−	1025.97i	−0.347002	−	0.347002i
$207$		−	428.840i		−	0.143993i
$208$	−105.687	−	2121.32i	−0.0352310	−	0.707151i
$209$	619.624	+	4607.13i	0.205073	+	1.52479i
$210$	−215.166	−	215.166i	−0.0707043	−	0.0707043i
$211$		−	235.549i		−	0.0768524i	−0.999261	−	0.0384262i	$-0.987766\pi$
$211$		−	235.549i		−	0.0768524i	0.999261	−	0.0384262i	$-0.0122344\pi$
$212$		−	1306.02i		−	0.423104i
$213$	1773.00	+	1773.00i	0.570347	+	0.570347i
$214$	2614.11	+	2614.11i	0.835031	+	0.835031i
$215$	250.164	+	250.164i	0.0793537	+	0.0793537i
$216$	−2388.83	−	2388.83i	−0.752497	−	0.752497i
$217$		−	977.418i		−	0.305767i
$218$		−	1092.10i		−	0.339294i
$219$	1555.62	+	1555.62i	0.479997	+	0.479997i
$220$	31.7219	+	235.864i	0.00972133	+	0.0722817i
$221$	−87.1568	−	1749.40i	−0.0265285	−	0.532476i
$222$		−	547.128i		−	0.165409i
$223$	2800.46	+	2800.46i	0.840954	+	0.840954i	0.988983	−	0.148029i	$-0.0472930\pi$
$223$	2800.46	+	2800.46i	0.840954	+	0.840954i	−0.148029	+	0.988983i	$0.547293\pi$
$224$	953.858			0.284519
$225$			1949.99i			0.577775i
$226$	45.7010	−	45.7010i	0.0134513	−	0.0134513i
$227$	3895.91	−	3895.91i	1.13912	−	1.13912i	0.150513	−	0.988608i	$-0.451908\pi$
$227$	3895.91	−	3895.91i	1.13912	−	1.13912i	0.988608	−	0.150513i	$-0.0480924\pi$
$228$	−531.738	−	531.738i	−0.154453	−	0.154453i
$229$	2763.59	−	2763.59i	0.797482	−	0.797482i	−0.185216	−	0.982698i	$-0.559298\pi$
$229$	2763.59	−	2763.59i	0.797482	−	0.797482i	0.982698	+	0.185216i	$0.0592985\pi$
$230$			212.232i			0.0608441i
$231$	1289.22	−	173.391i	0.367206	−	0.0493864i
$232$	−1335.72	+	1335.72i	−0.377992	+	0.377992i
$233$	−1394.23			−0.392013			−0.196007	−	0.980603i	$-0.562797\pi$
$233$	−1394.23			−0.392013			−0.196007	+	0.980603i	$0.562797\pi$
$234$	−1481.35	−	1340.75i	−0.413842	−	0.374563i
$235$	−1322.20			−0.367024
$236$	−908.183	−	908.183i	−0.250499	−	0.250499i
$237$			2757.32i			0.755726i
$238$	−1054.51			−0.287201
$239$	−645.403	+	645.403i	−0.174676	+	0.174676i	−0.789030	−	0.614354i	$-0.789417\pi$
$239$	−645.403	+	645.403i	−0.174676	+	0.174676i	0.614354	+	0.789030i	$0.289417\pi$
$240$	345.514	+	345.514i	0.0929286	+	0.0929286i
$241$	−586.337	−	586.337i	−0.156719	−	0.156719i	0.624392	−	0.781111i	$-0.285347\pi$
$241$	−586.337	−	586.337i	−0.156719	−	0.156719i	−0.781111	+	0.624392i	$0.785347\pi$
$242$	2858.49	+	1629.15i	0.759302	+	0.432751i
$243$	−3837.28			−1.01301
$244$	−238.843			−0.0626653
$245$	−519.203	+	519.203i	−0.135390	+	0.135390i
$246$			910.077i			0.235872i
$247$	−4428.04	−	4007.76i	−1.14069	−	1.03242i
$248$			2093.11i			0.535939i
$249$	1420.34	−	1420.34i	0.361488	−	0.361488i
$250$		−	2031.81i		−	0.514011i
$251$		−	3387.25i		−	0.851799i	−0.904770	−	0.425899i	$-0.859958\pi$
$251$		−	3387.25i		−	0.851799i	0.904770	−	0.425899i	$-0.140042\pi$
$252$	263.012	−	263.012i	0.0657468	−	0.0657468i
$253$	−721.333	−	550.307i	−0.179248	−	0.136749i
$254$	−3436.15	+	3436.15i	−0.848833	+	0.848833i
$255$	284.936	+	284.936i	0.0699741	+	0.0699741i
$256$	−2727.62			−0.665924
$257$		−	5756.16i		−	1.39712i	−0.715552	−	0.698559i	$-0.753825\pi$
$257$		−	5756.16i		−	1.39712i	0.715552	−	0.698559i	$-0.246175\pi$
$258$	−559.468	+	559.468i	−0.135004	+	0.135004i
$259$	808.945			0.194075
$260$	−226.696	−	205.179i	−0.0540733	−	0.0489410i
$261$			1332.48i			0.316008i
$262$	3938.66	+	3938.66i	0.928745	+	0.928745i
$263$		−	3538.85i		−	0.829713i	−0.909887	−	0.414857i	$-0.863832\pi$
$263$		−	3538.85i		−	0.829713i	0.909887	−	0.414857i	$-0.136168\pi$
$264$	−2760.84	+	371.311i	−0.643628	+	0.0865629i
$265$	1687.36	+	1687.36i	0.391147	+	0.391147i
$266$	−2542.48	+	2542.48i	−0.586051	+	0.586051i
$267$	−1636.76	+	1636.76i	−0.375160	+	0.375160i
$268$	−182.425	+	182.425i	−0.0415797	+	0.0415797i
$269$	671.219			0.152137			0.0760687	−	0.997103i	$-0.475763\pi$
$269$	671.219			0.152137			0.0760687	+	0.997103i	$0.475763\pi$
$270$	1179.36			0.265827
$271$	−3911.94	−	3911.94i	−0.876877	−	0.876877i	0.116333	−	0.993210i	$-0.462886\pi$
$271$	−3911.94	−	3911.94i	−0.876877	−	0.876877i	−0.993210	+	0.116333i	$0.962886\pi$
$272$	1693.33			0.377476
$273$	−1121.50	+	1239.11i	−0.248631	+	0.274704i
$274$		−	4651.29i		−	1.02553i
$275$	3279.99	+	2502.32i	0.719240	+	0.548710i
$276$	146.768			0.0320087
$277$	8143.38			1.76638			0.883192	−	0.469011i	$-0.155390\pi$
$277$	8143.38			1.76638			0.883192	+	0.469011i	$0.155390\pi$
$278$	5477.14	+	5477.14i	1.18164	+	1.18164i
$279$	1044.02	+	1044.02i	0.224028	+	0.224028i
$280$	−681.267	+	681.267i	−0.145405	+	0.145405i
$281$	2423.78	+	2423.78i	0.514557	+	0.514557i	0.915919	−	0.401363i	$-0.131463\pi$
$281$	2423.78	+	2423.78i	0.514557	+	0.514557i	−0.401363	+	0.915919i	$0.631463\pi$
$282$		−	2956.97i		−	0.624415i
$283$	2651.01			0.556843			0.278421	−	0.960459i	$-0.410189\pi$
$283$	2651.01			0.556843			0.278421	+	0.960459i	$0.410189\pi$
$284$	1072.57	−	1072.57i	0.224102	−	0.224102i
$285$	1373.99			0.285573
$286$	−4156.15	+	771.202i	−0.859296	+	0.159448i
$287$	−1345.58			−0.276749
$288$	−1018.85	+	1018.85i	−0.208460	+	0.208460i
$289$	−3516.55			−0.715765
$290$		−	659.438i		−	0.133529i
$291$	−3325.02	−	3325.02i	−0.669814	−	0.669814i
$292$	941.065	−	941.065i	0.188602	−	0.188602i
$293$	−4016.23	−	4016.23i	−0.800788	−	0.800788i	0.182431	−	0.983219i	$-0.441603\pi$
$293$	−4016.23	−	4016.23i	−0.800788	−	0.800788i	−0.983219	+	0.182431i	$0.941603\pi$
$294$	−1161.15	−	1161.15i	−0.230339	−	0.230339i
$295$	2346.72			0.463156
$296$	−1732.33			−0.340168
$297$	−3058.02	+	4008.40i	−0.597455	+	0.783134i
$298$		−	3447.41i		−	0.670145i
$299$	1164.21	−	58.0019i	0.225176	−	0.0112185i
$300$	−667.372			−0.128436
$301$	−827.191	−	827.191i	−0.158400	−	0.158400i
$302$	4107.04			0.782561
$303$	−298.389			−0.0565743
$304$	4082.72	−	4082.72i	0.770264	−	0.770264i
$305$	308.581	−	308.581i	0.0579321	−	0.0579321i
$306$	1126.36	−	1126.36i	0.210424	−	0.210424i
$307$	−2701.76	−	2701.76i	−0.502272	−	0.502272i	0.409872	−	0.912143i	$-0.365574\pi$
$307$	−2701.76	−	2701.76i	−0.502272	−	0.502272i	−0.912143	+	0.409872i	$0.865574\pi$
$308$	−104.892	−	779.908i	−0.0194051	−	0.144284i
$309$		−	1833.33i		−	0.337523i
$310$	−516.681	−	516.681i	−0.0946630	−	0.0946630i
$311$			1434.94i			0.261633i	0.991407	+	0.130816i	$0.0417598\pi$
$311$			1434.94i			0.261633i	−0.991407	+	0.130816i	$0.958240\pi$
$312$	2401.66	−	2653.51i	0.435792	−	0.481492i
$313$	−1977.71			−0.357146			−0.178573	−	0.983927i	$-0.557148\pi$
$313$	−1977.71			−0.357146			−0.178573	+	0.983927i	$0.557148\pi$
$314$	2474.99	−	2474.99i	0.444814	−	0.444814i
$315$			679.614i			0.121562i
$316$	1668.02			0.296942
$317$	313.519	+	313.519i	0.0555489	+	0.0555489i	0.734336	−	0.678787i	$-0.237494\pi$
$317$	313.519	+	313.519i	0.0555489	+	0.0555489i	−0.678787	+	0.734336i	$0.737494\pi$
$318$	−3773.63	+	3773.63i	−0.665454	+	0.665454i
$319$	2241.30	+	1709.89i	0.393381	+	0.300112i
$320$	1389.19	−	1389.19i	0.242681	−	0.242681i
$321$			4671.23i			0.812221i
$322$		−	701.765i		−	0.121453i
$323$	3366.91	−	3366.91i	0.579999	−	0.579999i
$324$			64.1589i			0.0110012i
$325$	−5293.79	+	263.742i	−0.903528	+	0.0450147i
$326$		−	5228.11i		−	0.888216i
$327$	975.751	−	975.751i	0.165013	−	0.165013i
$328$	2881.52			0.485077
$329$	4371.97			0.732628
$330$	589.850	−	773.165i	0.0983944	−	0.128974i
$331$	4269.58	+	4269.58i	0.708995	+	0.708995i	0.966324	−	0.257329i	$-0.0828423\pi$
$331$	4269.58	+	4269.58i	0.708995	+	0.708995i	−0.257329	+	0.966324i	$0.582842\pi$
$332$	−859.229	−	859.229i	−0.142037	−	0.142037i
$333$	−864.066	+	864.066i	−0.142194	+	0.142194i
$334$	−9621.53			−1.57625
$335$		−	471.379i		−	0.0768782i
$336$	−1142.48	−	1142.48i	−0.185498	−	0.185498i
$337$	1589.51			0.256931			0.128466	−	0.991714i	$-0.458995\pi$
$337$	1589.51			0.256931			0.128466	+	0.991714i	$0.458995\pi$
$338$	3439.48	−	4202.88i	0.553500	−	0.676350i
$339$	81.6646			0.0130838
$340$	172.371	−	172.371i	0.0274944	−	0.0274944i
$341$	3095.83	−	416.365i	0.491637	−	0.0661214i
$342$		−	5431.45i		−	0.858769i
$343$	4485.52	−	4485.52i	0.706108	−	0.706108i
$344$	1771.41	+	1771.41i	0.277639	+	0.277639i
$345$	−189.622	+	189.622i	−0.0295910	+	0.0295910i
$346$	1688.94	−	1688.94i	0.262422	−	0.262422i
$347$			5207.24i			0.805588i	0.915291	+	0.402794i	$0.131961\pi$
$347$			5207.24i			0.805588i	−0.915291	+	0.402794i	$0.868039\pi$
$348$	−456.032			−0.0702467
$349$	−7101.41	−	7101.41i	−1.08920	−	1.08920i	−0.995611	−	0.0935863i	$-0.970167\pi$
$349$	−7101.41	−	7101.41i	−1.08920	−	1.08920i	−0.0935863	−	0.995611i	$-0.529833\pi$
$350$			3191.01i			0.487334i
$351$	−322.313	−	6469.41i	−0.0490136	−	0.983793i
$352$	406.328	+	3021.20i	0.0615266	+	0.457473i
$353$	7625.93	+	7625.93i	1.14982	+	1.14982i	0.986587	+	0.163236i	$0.0521930\pi$
$353$	7625.93	+	7625.93i	1.14982	+	1.14982i	0.163236	+	0.986587i	$0.447807\pi$
$354$			5248.21i			0.787964i
$355$			2771.48i			0.414351i
$356$	990.146	+	990.146i	0.147409	+	0.147409i
$357$	−942.169	−	942.169i	−0.139678	−	0.139678i
$358$	5679.07	+	5679.07i	0.838402	+	0.838402i
$359$	8429.19	+	8429.19i	1.23921	+	1.23921i	0.960325	+	0.278883i	$0.0899642\pi$
$359$	8429.19	+	8429.19i	1.23921	+	1.23921i	0.278883	+	0.960325i	$0.410036\pi$
$360$		−	1455.37i		−	0.213069i
$361$		−	9376.61i		−	1.36705i
$362$	744.994	+	744.994i	0.108166	+	0.108166i
$363$	1098.38	+	4009.56i	0.158815	+	0.579745i
$364$	749.591	+	678.445i	0.107937	+	0.0976927i
$365$			2431.68i			0.348713i
$366$	690.113	+	690.113i	0.0985595	+	0.0985595i
$367$	8194.87			1.16558			0.582791	−	0.812622i	$-0.301960\pi$
$367$	8194.87			1.16558			0.582791	+	0.812622i	$0.301960\pi$
$368$			1126.89i			0.159629i
$369$	1437.26	−	1437.26i	0.202767	−	0.202767i
$370$	427.623	−	427.623i	0.0600840	−	0.0600840i
$371$	−5579.42	−	5579.42i	−0.780780	−	0.780780i
$372$	−357.309	+	357.309i	−0.0498000	+	0.0498000i
$373$			4778.39i			0.663313i	0.943400	+	0.331657i	$0.107608\pi$
$373$			4778.39i			0.663313i	−0.943400	+	0.331657i	$0.892392\pi$
$374$	−449.204	−	3340.00i	−0.0621064	−	0.461784i
$375$	1815.35	−	1815.35i	0.249985	−	0.249985i
$376$	−9362.45			−1.28413
$377$	−3617.37	+	180.221i	−0.494175	+	0.0246203i
$378$	−3899.66			−0.530626
$379$	6134.66	+	6134.66i	0.831442	+	0.831442i	0.987714	−	0.156272i	$-0.0499477\pi$
$379$	6134.66	+	6134.66i	0.831442	+	0.831442i	−0.156272	+	0.987714i	$0.549948\pi$
$380$		−	831.190i		−	0.112208i
$381$	−6140.18			−0.825645
$382$	−1687.15	+	1687.15i	−0.225974	+	0.225974i
$383$	−1997.52	−	1997.52i	−0.266497	−	0.266497i	0.561190	−	0.827687i	$-0.310344\pi$
$383$	−1997.52	−	1997.52i	−0.266497	−	0.266497i	−0.827687	+	0.561190i	$0.810344\pi$
$384$	1630.44	+	1630.44i	0.216674	+	0.216674i
$385$	1143.15	+	872.111i	0.151325	+	0.115446i
$386$	−3992.52			−0.526461
$387$	1767.11			0.232112
$388$	−2011.45	+	2011.45i	−0.263185	+	0.263185i
$389$		−	5873.09i		−	0.765495i	−0.923853	−	0.382747i	$-0.874978\pi$
$389$		−	5873.09i		−	0.765495i	0.923853	−	0.382747i	$-0.125022\pi$
$390$	62.1697	+	1247.86i	0.00807201	+	0.162020i
$391$			929.319i			0.120199i
$392$	−3676.47	+	3676.47i	−0.473698	+	0.473698i
$393$			7038.12i			0.903374i
$394$		−	10059.3i		−	1.28625i
$395$	−2155.06	+	2155.06i	−0.274514	+	0.274514i
$396$	945.089	+	721.011i	0.119931	+	0.0914954i
$397$	−4425.24	+	4425.24i	−0.559437	+	0.559437i	−0.929147	−	0.369710i	$-0.879457\pi$
$397$	−4425.24	+	4425.24i	−0.559437	+	0.559437i	0.369710	+	0.929147i	$0.379457\pi$
$398$	−4383.51	−	4383.51i	−0.552074	−	0.552074i
$399$	−4543.25			−0.570042
$400$		−	5124.13i		−	0.640516i
$401$	−918.617	+	918.617i	−0.114398	+	0.114398i	−0.761988	−	0.647591i	$-0.775777\pi$
$401$	−918.617	+	918.617i	−0.114398	+	0.114398i	0.647591	+	0.761988i	$0.275777\pi$
$402$	1054.20			0.130792
$403$	−2693.07	+	2975.48i	−0.332882	+	0.367790i
$404$			180.509i			0.0222293i
$405$	−82.8923	−	82.8923i	−0.0101703	−	0.0101703i
$406$			2180.50i			0.266542i
$407$	344.598	+	2562.21i	0.0419683	+	0.312050i
$408$	2017.63	+	2017.63i	0.244822	+	0.244822i
$409$	−6109.18	+	6109.18i	−0.738581	+	0.738581i	−0.972303	−	0.233722i	$-0.924909\pi$
$409$	−6109.18	+	6109.18i	−0.738581	+	0.738581i	0.233722	+	0.972303i	$0.424909\pi$
$410$	−711.297	+	711.297i	−0.0856792	+	0.0856792i
$411$	4155.77	−	4155.77i	0.498757	−	0.498757i
$412$	−1109.06			−0.132621
$413$	−7759.64			−0.924520
$414$	749.582	+	749.582i	0.0889854	+	0.0889854i
$415$	2220.22			0.262618
$416$	−2903.76	−	2628.15i	−0.342232	−	0.309749i
$417$			9787.28i			1.14936i
$418$	−9135.99	−	6969.88i	−1.06903	−	0.815569i
$419$	−7985.82			−0.931105			−0.465553	−	0.885020i	$-0.654144\pi$
$419$	−7985.82			−0.931105			−0.465553	+	0.885020i	$0.654144\pi$
$420$	−232.594			−0.0270224
$421$	−1752.22	−	1752.22i	−0.202846	−	0.202846i	0.598372	−	0.801218i	$-0.295814\pi$
$421$	−1752.22	−	1752.22i	−0.202846	−	0.202846i	−0.801218	+	0.598372i	$0.795814\pi$
$422$	411.722	+	411.722i	0.0474937	+	0.0474937i
$423$	−4669.87	+	4669.87i	−0.536777	+	0.536777i
$424$	11948.2	+	11948.2i	1.36853	+	1.36853i
$425$		−	4225.73i		−	0.482301i
$426$	−6198.15			−0.704933
$427$	−1020.35	+	1020.35i	−0.115640	+	0.115640i
$428$	2825.84			0.319140
$429$	−4402.43	−	3024.34i	−0.495457	−	0.340365i
$430$	−874.537			−0.0980788
$431$	7120.07	−	7120.07i	0.795735	−	0.795735i	−0.186685	−	0.982420i	$-0.559774\pi$
$431$	7120.07	−	7120.07i	0.795735	−	0.795735i	0.982420	+	0.186685i	$0.0597744\pi$
$432$	6262.07			0.697417
$433$			12461.1i			1.38301i	0.722373	+	0.691503i	$0.243051\pi$
$433$			12461.1i			1.38301i	−0.722373	+	0.691503i	$0.756949\pi$
$434$	1708.46	+	1708.46i	0.188960	+	0.188960i
$435$	589.186	−	589.186i	0.0649409	−	0.0649409i
$436$	−590.275	−	590.275i	−0.0648373	−	0.0648373i
$437$	2240.64	+	2240.64i	0.245273	+	0.245273i
$438$	−5438.23			−0.593262
$439$	−9585.56			−1.04213			−0.521064	−	0.853518i	$-0.674465\pi$
$439$	−9585.56			−1.04213			−0.521064	+	0.853518i	$0.674465\pi$
$440$	−2448.02	−	1867.60i	−0.265238	−	0.202351i
$441$			3667.55i			0.396021i
$442$	3210.17	+	2905.48i	0.345457	+	0.312668i
$443$	−9595.29			−1.02909			−0.514544	−	0.857464i	$-0.672039\pi$
$443$	−9595.29			−1.02909			−0.514544	+	0.857464i	$0.672039\pi$
$444$	−295.721	−	295.721i	−0.0316088	−	0.0316088i
$445$	−2558.51			−0.272550
$446$	−9790.00			−1.03939
$447$	3080.15	−	3080.15i	0.325919	−	0.325919i
$448$	−4593.49	+	4593.49i	−0.484424	+	0.484424i
$449$	2399.66	−	2399.66i	0.252221	−	0.252221i	−0.569660	−	0.821881i	$-0.692925\pi$
$449$	2399.66	−	2399.66i	0.252221	−	0.252221i	0.821881	+	0.569660i	$0.192925\pi$
$450$	−3408.44	−	3408.44i	−0.357057	−	0.357057i
$451$	−573.194	−	4261.91i	−0.0598463	−	0.444979i
$452$		−	49.4025i		−	0.00514093i
$453$	3669.50	+	3669.50i	0.380592	+	0.380592i
$454$			13619.5i			1.40792i
$455$	−1845.00	+	91.9198i	−0.190099	+	0.00947092i
$456$	9729.23			0.999152
$457$	−7785.05	+	7785.05i	−0.796870	+	0.796870i	−0.982601	−	0.185731i	$-0.940535\pi$
$457$	−7785.05	+	7785.05i	−0.796870	+	0.796870i	0.185731	+	0.982601i	$0.440535\pi$
$458$			9661.12i			0.985665i
$459$	5164.16			0.525147
$460$	114.711	+	114.711i	0.0116270	+	0.0116270i
$461$	−5864.59	+	5864.59i	−0.592497	+	0.592497i	−0.938305	−	0.345808i	$-0.887605\pi$
$461$	−5864.59	+	5864.59i	−0.592497	+	0.592497i	0.345808	+	0.938305i	$0.387605\pi$
$462$	−1950.39	+	2556.54i	−0.196408	+	0.257448i
$463$	196.068	−	196.068i	0.0196805	−	0.0196805i	−0.697198	−	0.716879i	$-0.745570\pi$
$463$	196.068	−	196.068i	0.0196805	−	0.0196805i	0.716879	+	0.697198i	$0.245570\pi$
$464$		−	3501.44i		−	0.350324i
$465$		−	923.275i		−	0.0920771i
$466$	2437.02	−	2437.02i	0.242259	−	0.242259i
$467$		−	2118.28i		−	0.209898i	−0.994478	−	0.104949i	$-0.966532\pi$
$467$		−	2118.28i		−	0.209898i	0.994478	−	0.104949i	$-0.0334680\pi$
$468$	−1525.34	+	75.9940i	−0.150660	+	0.00750603i
$469$			1558.66i			0.153459i
$470$	2311.10	−	2311.10i	0.226815	−	0.226815i
$471$	4422.64			0.432663
$472$	16617.1			1.62047
$473$	2267.63	−	2972.37i	0.220435	−	0.288943i
$474$	−4819.59	−	4819.59i	−0.467028	−	0.467028i
$475$	−10188.5	−	10188.5i	−0.984167	−	0.984167i
$476$	−569.960	+	569.960i	−0.0548825	+	0.0548825i
$477$	11919.2			1.14411
$478$		−	2256.23i		−	0.215895i
$479$	5348.84	+	5348.84i	0.510219	+	0.510219i	0.914593	−	0.404375i	$-0.132511\pi$
$479$	5348.84	+	5348.84i	0.510219	+	0.510219i	−0.404375	+	0.914593i	$0.632511\pi$
$480$	901.020			0.0856786
$481$	−2462.61	−	2228.88i	−0.233442	−	0.211285i
$482$	2049.75			0.193700
$483$	627.003	−	627.003i	0.0590676	−	0.0590676i
$484$	2425.56	−	664.457i	0.227795	−	0.0624020i
$485$		−	5197.52i		−	0.486613i
$486$	6707.29	−	6707.29i	0.626027	−	0.626027i
$487$	−8012.00	−	8012.00i	−0.745500	−	0.745500i	0.228131	−	0.973630i	$-0.426739\pi$
$487$	−8012.00	−	8012.00i	−0.745500	−	0.745500i	−0.973630	+	0.228131i	$0.926739\pi$
$488$	2185.06	−	2185.06i	0.202690	−	0.202690i
$489$	4671.14	−	4671.14i	0.431976	−	0.431976i
$490$		−	1815.06i		−	0.167339i
$491$	−9994.58			−0.918634			−0.459317	−	0.888272i	$-0.651906\pi$
$491$	−9994.58			−0.918634			−0.459317	+	0.888272i	$0.651906\pi$
$492$	491.894	+	491.894i	0.0450738	+	0.0450738i
$493$		−	2887.54i		−	0.263790i
$494$	14745.2	−	734.619i	1.34295	−	0.0669070i
$495$	−2152.58	+	289.505i	−0.195457	+	0.0262874i
$496$	−2743.44	−	2743.44i	−0.248355	−	0.248355i
$497$		−	9164.16i		−	0.827100i
$498$			4965.31i			0.446789i
$499$	4180.02	+	4180.02i	0.374997	+	0.374997i	0.869293	−	0.494297i	$-0.164574\pi$
$499$	4180.02	+	4180.02i	0.374997	+	0.374997i	−0.494297	+	0.869293i	$0.664574\pi$
$500$	−1098.19	−	1098.19i	−0.0982247	−	0.0982247i
$501$	−8596.51	−	8596.51i	−0.766595	−	0.766595i
$502$	5920.67	+	5920.67i	0.526400	+	0.526400i
$503$		−	7502.94i		−	0.665088i	−0.943088	−	0.332544i	$-0.892093\pi$
$503$		−	7502.94i		−	0.665088i	0.943088	−	0.332544i	$-0.107907\pi$
$504$			4812.34i			0.425314i
$505$	−233.214	−	233.214i	−0.0205503	−	0.0205503i
$506$	2222.73	−	298.941i	0.195282	−	0.0262639i
$507$	6828.19	−	682.068i	0.598127	−	0.0597470i
$508$			3714.46i			0.324415i
$509$	−2851.36	−	2851.36i	−0.248299	−	0.248299i	0.571973	−	0.820272i	$-0.306178\pi$
$509$	−2851.36	−	2851.36i	−0.248299	−	0.248299i	−0.820272	+	0.571973i	$0.806178\pi$
$510$	−996.096			−0.0864860
$511$		−	8040.59i		−	0.696076i
$512$	8943.71	−	8943.71i	0.771992	−	0.771992i
$513$	12451.1	−	12451.1i	1.07160	−	1.07160i
$514$	10061.4	+	10061.4i	0.863399	+	0.863399i
$515$	1432.89	−	1432.89i	0.122604	−	0.122604i
$516$			604.782i			0.0515970i
$517$	1862.39	+	13847.6i	0.158429	+	1.17798i
$518$	−1413.98	+	1413.98i	−0.119936	+	0.119936i
$519$	3018.03			0.255254
$520$	3951.01	−	196.844i	0.333199	−	0.0166003i
$521$	−6305.71			−0.530246			−0.265123	−	0.964215i	$-0.585413\pi$
$521$	−6305.71			−0.530246			−0.265123	+	0.964215i	$0.585413\pi$
$522$	−2329.07	−	2329.07i	−0.195289	−	0.195289i
$523$		−	14552.1i		−	1.21667i	−0.793679	−	0.608337i	$-0.791837\pi$
$523$		−	14552.1i		−	1.21667i	0.793679	−	0.608337i	$-0.208163\pi$
$524$	4257.67			0.354956
$525$	−2851.06	+	2851.06i	−0.237011	+	0.237011i
$526$	6185.65	+	6185.65i	0.512751	+	0.512751i
$527$	−2262.44	−	2262.44i	−0.187008	−	0.187008i
$528$	3131.95	−	4105.30i	0.258145	−	0.338372i
$529$	11548.5			0.949170
$530$	−5898.77			−0.483446
$531$	8288.37	−	8288.37i	0.677372	−	0.677372i
$532$			2748.41i			0.223983i
$533$	4096.24	+	3707.45i	0.332885	+	0.301290i
$534$		−	5721.86i		−	0.463687i
$535$	−3650.94	+	3650.94i	−0.295035	+	0.295035i
$536$		−	3337.83i		−	0.268978i
$537$			10148.1i			0.815500i
$538$	−1173.24	+	1173.24i	−0.0940187	+	0.0940187i
$539$	6169.02	+	4706.36i	0.492984	+	0.376099i
$540$	637.440	−	637.440i	0.0507982	−	0.0507982i
$541$	−13791.5	−	13791.5i	−1.09601	−	1.09601i	−0.994872	−	0.101140i	$-0.967751\pi$
$541$	−13791.5	−	13791.5i	−1.09601	−	1.09601i	−0.101140	−	0.994872i	$-0.532249\pi$
$542$	13675.6			1.08379
$543$			1331.25i			0.105211i
$544$	2207.91	−	2207.91i	0.174013	−	0.174013i
$545$	1525.25			0.119880
$546$	−205.570	−	4126.17i	−0.0161128	−	0.323413i
$547$			13998.6i			1.09422i	0.837062	+	0.547108i	$0.184271\pi$
$547$			13998.6i			1.09422i	−0.837062	+	0.547108i	$0.815729\pi$
$548$	−2514.01	−	2514.01i	−0.195973	−	0.195973i
$549$		−	2179.76i		−	0.169453i
$550$	−10107.1	+	1359.32i	−0.783575	+	0.105385i
$551$	−6962.03	−	6962.03i	−0.538280	−	0.538280i
$552$	−1342.71	+	1342.71i	−0.103532	+	0.103532i
$553$	7125.91	−	7125.91i	0.547965	−	0.547965i
$554$	−14234.0	+	14234.0i	−1.09160	+	1.09160i
$555$	764.134			0.0584427
$556$	5920.76			0.451611
$557$	1171.48	+	1171.48i	0.0891156	+	0.0891156i	0.750259	−	0.661144i	$-0.229929\pi$
$557$	1171.48	+	1171.48i	0.0891156	+	0.0891156i	−0.661144	+	0.750259i	$0.729929\pi$
$558$	−3649.74			−0.276892
$559$	239.007	+	4797.30i	0.0180839	+	0.362977i
$560$		−	1785.87i		−	0.134762i
$561$	2582.83	−	3385.53i	0.194380	−	0.254790i
$562$	−8473.17			−0.635977
$563$	16605.0			1.24302			0.621509	−	0.783407i	$-0.286520\pi$
$563$	16605.0			1.24302			0.621509	+	0.783407i	$0.286520\pi$
$564$	−1598.23	−	1598.23i	−0.119322	−	0.119322i
$565$	63.8273	+	63.8273i	0.00475263	+	0.00475263i
$566$	−4633.78	+	4633.78i	−0.344121	+	0.344121i
$567$	274.091	+	274.091i	0.0203012	+	0.0203012i
$568$			19624.8i			1.44971i
$569$	7191.89			0.529876			0.264938	−	0.964265i	$-0.414648\pi$
$569$	7191.89			0.529876			0.264938	+	0.964265i	$0.414648\pi$
$570$	−2401.64	+	2401.64i	−0.176480	+	0.176480i
$571$	−9700.08			−0.710921			−0.355460	−	0.934691i	$-0.615676\pi$
$571$	−9700.08			−0.710921			−0.355460	+	0.934691i	$0.615676\pi$
$572$	−1829.56	+	2663.22i	−0.133737	+	0.194676i
$573$	−3014.82			−0.219801
$574$	2351.97	−	2351.97i	0.171027	−	0.171027i
$575$	2812.18			0.203958
$576$		−	9812.96i		−	0.709849i
$577$	−7643.57	−	7643.57i	−0.551483	−	0.551483i	0.375385	−	0.926869i	$-0.377510\pi$
$577$	−7643.57	−	7643.57i	−0.551483	−	0.551483i	−0.926869	+	0.375385i	$0.877510\pi$
$578$	6146.68	−	6146.68i	0.442333	−	0.442333i
$579$	−3567.19	−	3567.19i	−0.256040	−	0.256040i
$580$	−356.425	−	356.425i	−0.0255168	−	0.0255168i
$581$	−7341.37			−0.524219
$582$	11623.8			0.827871
$583$	15295.2	−	20048.7i	1.08656	−	1.42424i
$584$			17218.7i			1.22006i
$585$	1872.53	−	2068.90i	0.132341	−	0.146220i
$586$	14040.2			0.989750
$587$	−4889.31	−	4889.31i	−0.343788	−	0.343788i	0.514002	−	0.857789i	$-0.328163\pi$
$587$	−4889.31	−	4889.31i	−0.343788	−	0.343788i	−0.857789	+	0.514002i	$0.828163\pi$
$588$	−1255.20			−0.0880330
$589$	−10909.7			−0.763206
$590$	−4101.89	+	4101.89i	−0.286224	+	0.286224i
$591$	8987.66	−	8987.66i	0.625555	−	0.625555i
$592$	2270.57	−	2270.57i	0.157635	−	0.157635i
$593$	1506.79	+	1506.79i	0.104345	+	0.104345i	0.757352	−	0.653007i	$-0.226493\pi$
$593$	1506.79	+	1506.79i	0.104345	+	0.104345i	−0.653007	+	0.757352i	$0.726493\pi$
$594$	−1661.19	−	12351.6i	−0.114747	−	0.853184i
$595$		−	1472.76i		−	0.101474i
$596$	−1863.32	−	1863.32i	−0.128061	−	0.128061i
$597$		−	7833.03i		−	0.536993i
$598$	−1933.56	+	2136.33i	−0.132223	+	0.146089i
$599$	−11194.9			−0.763626			−0.381813	−	0.924240i	$-0.624700\pi$
$599$	−11194.9			−0.763626			−0.381813	+	0.924240i	$0.624700\pi$
$600$	6105.47	−	6105.47i	0.415425	−	0.415425i
$601$			24225.5i			1.64423i	0.569324	+	0.822113i	$0.307205\pi$
$601$			24225.5i			1.64423i	−0.569324	+	0.822113i	$0.692795\pi$
$602$	2891.74			0.195778
$603$	−1664.87	−	1664.87i	−0.112435	−	0.112435i
$604$	2219.84	−	2219.84i	0.149543	−	0.149543i
$605$	−2275.32	+	3992.25i	−0.152901	+	0.268278i
$606$	521.562	−	521.562i	0.0349621	−	0.0349621i
$607$			3153.50i			0.210868i	0.994426	+	0.105434i	$0.0336231\pi$
$607$			3153.50i			0.210868i	−0.994426	+	0.105434i	$0.966377\pi$
$608$		−	10646.8i		−	0.710170i
$609$	−1948.20	+	1948.20i	−0.129631	+	0.129631i
$610$			1078.75i			0.0716024i
$611$	−13309.3	−	12046.0i	−0.881235	−	0.797594i
$612$		−	1217.59i		−	0.0804220i
$613$	−5789.38	+	5789.38i	−0.381453	+	0.381453i	−0.871625	−	0.490172i	$-0.836934\pi$
$613$	−5789.38	+	5789.38i	−0.381453	+	0.381453i	0.490172	+	0.871625i	$0.336934\pi$
$614$	9444.95			0.620793
$615$	−1271.04			−0.0833387
$616$	8094.61	+	6175.40i	0.529450	+	0.403919i
$617$	94.0583	+	94.0583i	0.00613719	+	0.00613719i	0.710169	−	0.704032i	$-0.248619\pi$
$617$	94.0583	+	94.0583i	0.00613719	+	0.00613719i	−0.704032	+	0.710169i	$0.748619\pi$
$618$	3204.53	+	3204.53i	0.208584	+	0.208584i
$619$	−2224.62	+	2224.62i	−0.144451	+	0.144451i	−0.775634	−	0.631183i	$-0.782570\pi$
$619$	−2224.62	+	2224.62i	−0.144451	+	0.144451i	0.631183	+	0.775634i	$0.282570\pi$
$620$	−558.530			−0.0361792
$621$			3436.69i			0.222077i
$622$	−2508.17	−	2508.17i	−0.161685	−	0.161685i
$623$	8459.94			0.544046
$624$	330.105	+	6625.81i	0.0211775	+	0.425071i
$625$	−11297.5			−0.723037
$626$	3456.89	−	3456.89i	0.220711	−	0.220711i
$627$	−1935.35	−	14390.0i	−0.123270	−	0.916560i
$628$		−	2675.45i		−	0.170003i
$629$	1872.47	−	1872.47i	0.118697	−	0.118697i
$630$	−1187.92	−	1187.92i	−0.0751234	−	0.0751234i
$631$	−16360.7	+	16360.7i	−1.03219	+	1.03219i	−0.0327213	+	0.999465i	$0.510417\pi$
$631$	−16360.7	+	16360.7i	−1.03219	+	1.03219i	−0.999465	+	0.0327213i	$0.989583\pi$
$632$	−15259.9	+	15259.9i	−0.960456	+	0.960456i
$633$			735.720i			0.0461963i
$634$	−1096.02			−0.0686568
$635$	−4799.03	−	4799.03i	−0.299911	−	0.299911i
$636$			4079.27i			0.254330i
$637$	−9956.57	+	496.047i	−0.619299	+	0.0308541i
$638$	−6906.39	+	928.856i	−0.428568	+	0.0576391i
$639$	9788.59	+	9788.59i	0.605995	+	0.605995i
$640$			2548.63i			0.157412i
$641$		−	6268.29i		−	0.386244i	−0.981175	−	0.193122i	$-0.938139\pi$
$641$		−	6268.29i		−	0.386244i	0.981175	−	0.193122i	$-0.0618613\pi$
$642$	−8164.98	−	8164.98i	−0.501941	−	0.501941i
$643$	−738.102	−	738.102i	−0.0452689	−	0.0452689i	0.684110	−	0.729379i	$-0.260191\pi$
$643$	−738.102	−	738.102i	−0.0452689	−	0.0452689i	−0.729379	+	0.684110i	$0.760191\pi$
$644$	−379.302	−	379.302i	−0.0232090	−	0.0232090i
$645$	−781.369	−	781.369i	−0.0476998	−	0.0476998i
$646$			11770.2i			0.716863i
$647$			27427.5i			1.66659i	0.552826	+	0.833297i	$0.313549\pi$
$647$			27427.5i			1.66659i	−0.552826	+	0.833297i	$0.686451\pi$
$648$	−586.959	−	586.959i	−0.0355832	−	0.0355832i
$649$	−3305.48	−	24577.5i	−0.199925	−	1.48652i
$650$	8792.15	−	9714.16i	0.530549	−	0.586186i
$651$			3052.90i			0.183798i
$652$	−2825.78	−	2825.78i	−0.169733	−	0.169733i
$653$	−3266.52			−0.195756			−0.0978780	−	0.995198i	$-0.531205\pi$
$653$	−3266.52			−0.195756			−0.0978780	+	0.995198i	$0.531205\pi$
$654$			3411.08i			0.203951i
$655$	−5500.84	+	5500.84i	−0.328146	+	0.328146i
$656$	−3776.80	+	3776.80i	−0.224785	+	0.224785i
$657$	8588.47	+	8588.47i	0.509997	+	0.509997i
$658$	−7641.89	+	7641.89i	−0.452753	+	0.452753i
$659$			4458.12i			0.263526i	0.991281	+	0.131763i	$0.0420638\pi$
$659$			4458.12i			0.263526i	−0.991281	+	0.131763i	$0.957936\pi$
$660$	−99.0812	−	736.706i	−0.00584353	−	0.0434488i
$661$	−14096.0	+	14096.0i	−0.829454	+	0.829454i	−0.987441	−	0.157987i	$-0.949500\pi$
$661$	−14096.0	+	14096.0i	−0.829454	+	0.829454i	0.157987	+	0.987441i	$0.449500\pi$
$662$	−14925.8			−0.876298
$663$	272.228	+	5464.12i	0.0159464	+	0.320074i
$664$	15721.3			0.918835
$665$	−3550.90	−	3550.90i	−0.207065	−	0.207065i
$666$		−	3020.65i		−	0.175747i
$667$	1921.63			0.111553
$668$	−5200.41	+	5200.41i	−0.301213	+	0.301213i
$669$	−8747.04	−	8747.04i	−0.505501	−	0.505501i
$670$	823.937	+	823.937i	0.0475096	+	0.0475096i
$671$	−3666.47	−	2797.16i	−0.210943	−	0.160929i
$672$	−2979.31			−0.171026
$673$	29459.5			1.68734			0.843671	−	0.536860i	$-0.180390\pi$
$673$	29459.5			1.68734			0.843671	+	0.536860i	$0.180390\pi$
$674$	−2778.34	+	2778.34i	−0.158780	+	0.158780i
$675$		−	15627.1i		−	0.891091i
$676$	−412.613	−	4130.67i	−0.0234759	−	0.235018i
$677$		−	26414.9i		−	1.49957i	−0.661682	−	0.749785i	$-0.730157\pi$
$677$		−	26414.9i		−	1.49957i	0.661682	−	0.749785i	$-0.269843\pi$
$678$	−142.744	+	142.744i	−0.00808561	+	0.00808561i
$679$			17186.1i			0.971343i
$680$			3153.87i			0.177861i
$681$	−12168.6	+	12168.6i	−0.684730	+	0.684730i
$682$	−4683.50	+	6139.05i	−0.262963	+	0.344687i
$683$	24574.3	−	24574.3i	1.37674	−	1.37674i	0.526660	−	0.850076i	$-0.323444\pi$
$683$	24574.3	−	24574.3i	1.37674	−	1.37674i	0.850076	−	0.526660i	$-0.176556\pi$
$684$	−2935.68	−	2935.68i	−0.164106	−	0.164106i
$685$	6496.12			0.362342
$686$			15680.7i			0.872730i
$687$	−8631.88	+	8631.88i	−0.479370	+	0.479370i
$688$	−4643.56			−0.257317
$689$	1612.11	+	32357.9i	0.0891384	+	1.78917i
$690$		−	662.891i		−	0.0365737i
$691$	3919.81	+	3919.81i	0.215798	+	0.215798i	0.806725	−	0.590927i	$-0.201238\pi$
$691$	3919.81	+	3919.81i	0.215798	+	0.215798i	−0.590927	+	0.806725i	$0.701238\pi$
$692$		−	1825.74i		−	0.100295i
$693$	7117.70	−	957.275i	0.390157	−	0.0524731i
$694$	−9101.87	−	9101.87i	−0.497842	−	0.497842i
$695$	−7649.52	+	7649.52i	−0.417501	+	0.417501i
$696$	4172.01	−	4172.01i	0.227212	−	0.227212i
$697$	−3114.62	+	3114.62i	−0.169261	+	0.169261i
$698$	24825.5			1.34622
$699$	4354.78			0.235641
$700$	1724.73	+	1724.73i	0.0931269	+	0.0931269i
$701$	21565.6			1.16194			0.580970	−	0.813925i	$-0.302673\pi$
$701$	21565.6			1.16194			0.580970	+	0.813925i	$0.302673\pi$
$702$	11871.4	+	10744.7i	0.638260	+	0.577680i
$703$		−	9029.28i		−	0.484418i
$704$	−16505.9	−	12592.4i	−0.883651	−	0.674140i
$705$	4129.79			0.220620
$706$	−26659.1			−1.42115
$707$	771.146	+	771.146i	0.0410211	+	0.0410211i
$708$	2836.64	+	2836.64i	0.150576	+	0.150576i
$709$	23432.8	−	23432.8i	1.24124	−	1.24124i	0.281752	−	0.959487i	$-0.409084\pi$
$709$	23432.8	−	23432.8i	1.24124	−	1.24124i	0.959487	−	0.281752i	$-0.0909157\pi$
$710$	−4844.34	−	4844.34i	−0.256063	−	0.256063i
$711$			15222.9i			0.802960i
$712$	−18116.7			−0.953586
$713$	1505.63	−	1505.63i	0.0790831	−	0.0790831i
$714$	3293.69			0.172637
$715$	−1077.08	−	5804.60i	−0.0563365	−	0.303608i
$716$	6139.04			0.320428
$717$	2015.87	−	2015.87i	0.104999	−	0.104999i
$718$	−29467.2			−1.53163
$719$			5505.35i			0.285556i	0.989755	+	0.142778i	$0.0456035\pi$
$719$			5505.35i			0.285556i	−0.989755	+	0.142778i	$0.954396\pi$
$720$	1907.56	+	1907.56i	0.0987367	+	0.0987367i
$721$	−4738.00	+	4738.00i	−0.244733	+	0.244733i
$722$	16389.6	+	16389.6i	0.844819	+	0.844819i
$723$	1831.38	+	1831.38i	0.0942045	+	0.0942045i
$724$	805.334			0.0413398
$725$	−8737.88			−0.447610
$726$	−8928.30	−	5088.54i	−0.456419	−	0.260128i
$727$		−	17119.9i		−	0.873371i	−0.899614	−	0.436685i	$-0.856152\pi$
$727$		−	17119.9i		−	0.873371i	0.899614	−	0.436685i	$-0.143848\pi$
$728$	−13064.4	+	650.882i	−0.665109	+	0.0331364i
$729$	11068.7			0.562347
$730$	−4250.41	−	4250.41i	−0.215499	−	0.215499i
$731$	−3829.42			−0.193757
$732$	746.008			0.0376684
$733$	−16266.2	+	16266.2i	−0.819653	+	0.819653i	−0.986058	−	0.166404i	$-0.946784\pi$
$733$	−16266.2	+	16266.2i	−0.819653	+	0.819653i	0.166404	+	0.986058i	$0.446784\pi$
$734$	−14324.0	+	14324.0i	−0.720313	+	0.720313i
$735$	1621.69	−	1621.69i	0.0813838	−	0.0813838i
$736$	1469.34	+	1469.34i	0.0735876	+	0.0735876i
$737$	−4936.82	+	663.965i	−0.246744	+	0.0331852i
$738$			5024.46i			0.250614i
$739$	10150.6	+	10150.6i	0.505273	+	0.505273i	0.913072	−	0.407799i	$-0.133703\pi$
$739$	10150.6	+	10150.6i	0.505273	+	0.505273i	−0.407799	+	0.913072i	$0.633703\pi$
$740$		−	462.259i		−	0.0229635i
$741$	13830.7	+	12517.9i	0.685671	+	0.620591i
$742$	19504.9			0.965021
$743$	−6451.29	+	6451.29i	−0.318540	+	0.318540i	−0.848206	−	0.529666i	$-0.822317\pi$
$743$	−6451.29	+	6451.29i	−0.318540	+	0.318540i	0.529666	+	0.848206i	$0.322317\pi$
$744$		−	6537.69i		−	0.322155i
$745$	4814.75			0.236777
$746$	−8352.29	−	8352.29i	−0.409918	−	0.409918i
$747$	7841.60	−	7841.60i	0.384082	−	0.384082i
$748$	−2048.06	−	1562.47i	−0.100113	−	0.0763763i
$749$	12072.2	−	12072.2i	0.588928	−	0.588928i
$750$			6346.20i			0.308974i
$751$			19444.3i			0.944784i	0.881389	+	0.472392i	$0.156609\pi$
$751$			19444.3i			0.944784i	−0.881389	+	0.472392i	$0.843391\pi$
$752$	12271.3	−	12271.3i	0.595066	−	0.595066i
$753$			10579.8i			0.512020i
$754$	6007.89	−	6637.92i	0.290178	−	0.320608i
$755$			5736.01i			0.276496i
$756$	−2107.75	+	2107.75i	−0.101400	+	0.101400i
$757$	−32057.9			−1.53919			−0.769593	−	0.638534i	$-0.779541\pi$
$757$	−32057.9			−1.53919			−0.769593	+	0.638534i	$0.779541\pi$
$758$	−21445.9			−1.02764
$759$	2253.03	+	1718.84i	0.107747	+	0.0822004i
$760$	7604.16	+	7604.16i	0.362937	+	0.362937i
$761$	3072.30	+	3072.30i	0.146348	+	0.146348i	0.776484	−	0.630136i	$-0.217001\pi$
$761$	3072.30	+	3072.30i	0.146348	+	0.146348i	−0.630136	+	0.776484i	$0.717001\pi$
$762$	10732.6	−	10732.6i	0.510237	−	0.510237i
$763$	−5043.39			−0.239296
$764$			1823.80i			0.0863648i
$765$	1573.11	+	1573.11i	0.0743476	+	0.0743476i
$766$	6983.03			0.329383
$767$	23622.1	+	21380.0i	1.11205	+	1.00650i
$768$	8519.54			0.400289
$769$	−5423.68	+	5423.68i	−0.254334	+	0.254334i	−0.822745	−	0.568411i	$-0.807558\pi$
$769$	−5423.68	+	5423.68i	−0.254334	+	0.254334i	0.568411	+	0.822745i	$0.307558\pi$
$770$	−3522.53	+	473.753i	−0.164861	+	0.0221725i
$771$			17979.0i			0.839814i
$772$	−2157.95	+	2157.95i	−0.100604	+	0.100604i
$773$	−9711.37	−	9711.37i	−0.451868	−	0.451868i	0.444106	−	0.895974i	$-0.353521\pi$
$773$	−9711.37	−	9711.37i	−0.451868	−	0.451868i	−0.895974	+	0.444106i	$0.853521\pi$
$774$	−3088.78	+	3088.78i	−0.143442	+	0.143442i
$775$	−6846.28	+	6846.28i	−0.317324	+	0.317324i
$776$		−	36803.6i		−	1.70254i
$777$	−2526.68			−0.116659
$778$	10265.7	+	10265.7i	0.473065	+	0.473065i
$779$			15019.1i			0.690775i
$780$	708.068	+	640.862i	0.0325037	+	0.0294187i
$781$	29026.1	−	3903.78i	1.32988	−	0.178858i
$782$	−1624.38	−	1624.38i	−0.0742811	−	0.0742811i
$783$		−	10678.4i		−	0.487373i
$784$		−	9637.48i		−	0.439025i
$785$	3456.64	+	3456.64i	0.157163	+	0.157163i
$786$	−12302.1	−	12302.1i	−0.558272	−	0.558272i
$787$	3511.22	+	3511.22i	0.159036	+	0.159036i	0.782139	−	0.623103i	$-0.214128\pi$
$787$	3511.22	+	3511.22i	0.159036	+	0.159036i	−0.623103	+	0.782139i	$0.714128\pi$
$788$	−5437.03	−	5437.03i	−0.245795	−	0.245795i
$789$			11053.3i			0.498744i
$790$		−	7533.78i		−	0.339291i
$791$	−211.051	−	211.051i	−0.00948687	−	0.00948687i
$792$	−15242.4	+	2049.98i	−0.683855	+	0.0919732i
$793$	5917.55	−	294.818i	0.264992	−	0.0132022i
$794$		−	15470.0i		−	0.691449i
$795$	−5270.36	−	5270.36i	−0.235120	−	0.235120i
$796$	−4738.55			−0.210997
$797$			27158.3i			1.20702i	0.797355	+	0.603510i	$0.206232\pi$
$797$			27158.3i			1.20702i	−0.797355	+	0.603510i	$0.793768\pi$
$798$	7941.26	−	7941.26i	0.352278	−	0.352278i
$799$	10119.8	−	10119.8i	0.448078	−	0.448078i
$800$	−6681.26	−	6681.26i	−0.295273	−	0.295273i
$801$	−9036.39	+	9036.39i	−0.398608	+	0.398608i
$802$		−	3211.35i		−	0.141392i
$803$	25467.4	−	3425.16i	1.11921	−	0.150525i
$804$	569.790	−	569.790i	0.0249937	−	0.0249937i
$805$	980.105			0.0429120
$806$	−493.637	−	9908.21i	−0.0215727	−	0.433005i
$807$	−2096.50			−0.0914504
$808$	−1651.39	−	1651.39i	−0.0719005	−	0.0719005i
$809$		−	39619.3i		−	1.72181i	−0.508769	−	0.860903i	$-0.669899\pi$
$809$		−	39619.3i		−	1.72181i	0.508769	−	0.860903i	$-0.330101\pi$
$810$	289.780			0.0125701
$811$	−8988.92	+	8988.92i	−0.389203	+	0.389203i	−0.874403	−	0.485200i	$-0.838747\pi$
$811$	−8988.92	+	8988.92i	−0.389203	+	0.389203i	0.485200	+	0.874403i	$0.338747\pi$
$812$	1178.55	+	1178.55i	0.0509348	+	0.0509348i
$813$	12218.7	+	12218.7i	0.527094	+	0.527094i
$814$	−5080.89	−	3876.23i	−0.218778	−	0.166906i
$815$	7301.73			0.313826
$816$	−5289.00			−0.226902
$817$	−9232.94	+	9232.94i	−0.395373	+	0.395373i
$818$		−	21356.8i		−	0.912865i
$819$	−6191.71	+	6841.01i	−0.264171	+	0.291873i
$820$			768.908i			0.0327457i
$821$	9218.75	−	9218.75i	0.391884	−	0.391884i	−0.483475	−	0.875358i	$-0.660625\pi$
$821$	9218.75	−	9218.75i	0.391884	−	0.391884i	0.875358	+	0.483475i	$0.160625\pi$
$822$			14528.0i			0.616449i
$823$		−	27419.0i		−	1.16132i	−0.814146	−	0.580661i	$-0.802794\pi$
$823$		−	27419.0i		−	1.16132i	0.814146	−	0.580661i	$-0.197206\pi$
$824$	10146.3	−	10146.3i	0.428960	−	0.428960i
$825$	−10244.8	−	7815.80i	−0.432338	−	0.329832i
$826$	13563.3	−	13563.3i	0.571340	−	0.571340i
$827$	15049.5	+	15049.5i	0.632794	+	0.632794i	0.948768	−	0.315974i	$-0.102331\pi$
$827$	15049.5	+	15049.5i	0.632794	+	0.632794i	−0.315974	+	0.948768i	$0.602331\pi$
$828$	810.294			0.0340093
$829$			41934.0i			1.75685i	0.477879	+	0.878426i	$0.341406\pi$
$829$			41934.0i			1.75685i	−0.477879	+	0.878426i	$0.658594\pi$
$830$	−3880.78	+	3880.78i	−0.162294	+	0.162294i
$831$	−25435.3			−1.06178
$832$	26640.0	−	1327.23i	1.11007	−	0.0553046i
$833$		−	7947.77i		−	0.330581i
$834$	−17107.4	−	17107.4i	−0.710291	−	0.710291i
$835$		−	13437.7i		−	0.556923i
$836$	−8705.18	+	1170.78i	−0.360137	+	0.0484357i
$837$	−8366.68	−	8366.68i	−0.345513	−	0.345513i
$838$	13958.6	−	13958.6i	0.575410	−	0.575410i
$839$	8705.77	−	8705.77i	0.358232	−	0.358232i	−0.504929	−	0.863161i	$-0.668481\pi$
$839$	8705.77	−	8705.77i	0.358232	−	0.358232i	0.863161	+	0.504929i	$0.168481\pi$
$840$	2127.89	−	2127.89i	0.0874037	−	0.0874037i
$841$	18418.2			0.755184
$842$	6125.52			0.250712
$843$	−7570.49	−	7570.49i	−0.309302	−	0.309302i
$844$	445.070			0.0181516
$845$	5869.86	+	4803.68i	0.238970	+	0.195564i
$846$		−	16325.2i		−	0.663441i
$847$	7523.56	−	13200.8i	0.305210	−	0.535518i
$848$	−31320.9			−1.26835
$849$	−8280.25			−0.334720
$850$	7386.27	+	7386.27i	0.298055	+	0.298055i
$851$	1246.11	+	1246.11i	0.0501952	+	0.0501952i
$852$	−3350.08	+	3350.08i	−0.134709	+	0.134709i
$853$	−25819.6	−	25819.6i	−1.03640	−	1.03640i	−0.999312	−	0.0370841i	$-0.988193\pi$
$853$	−25819.6	−	25819.6i	−1.03640	−	1.03640i	−0.0370841	−	0.999312i	$-0.511807\pi$
$854$		−	3567.01i		−	0.142928i
$855$	7585.71			0.303422
$856$	−25852.2	+	25852.2i	−1.03226	+	1.03226i
$857$	28498.9			1.13594			0.567971	−	0.823048i	$-0.307729\pi$
$857$	28498.9			1.13594			0.567971	+	0.823048i	$0.307729\pi$
$858$	12981.4	−	2408.79i	0.516526	−	0.0958448i
$859$	−22345.5			−0.887566			−0.443783	−	0.896134i	$-0.646364\pi$
$859$	−22345.5			−0.887566			−0.443783	+	0.896134i	$0.646364\pi$
$860$	−472.685	+	472.685i	−0.0187423	+	0.0187423i
$861$	4202.81			0.166355
$862$			24890.7i			0.983505i
$863$	−1890.53	−	1890.53i	−0.0745705	−	0.0745705i	0.668838	−	0.743408i	$-0.266792\pi$
$863$	−1890.53	−	1890.53i	−0.0745705	−	0.0745705i	−0.743408	+	0.668838i	$0.766792\pi$
$864$	8165.00	−	8165.00i	0.321504	−	0.321504i
$865$	2358.83	+	2358.83i	0.0927196	+	0.0927196i
$866$	−21781.1	−	21781.1i	−0.854678	−	0.854678i
$867$	10983.7			0.430249
$868$	1846.83			0.0722184
$869$	25605.8	+	19534.7i	0.999559	+	0.762567i
$870$			2059.71i			0.0802651i
$871$	4294.56	−	4744.91i	0.167067	−	0.184587i
$872$	10800.3			0.419431
$873$	−18357.1	−	18357.1i	−0.711678	−	0.711678i
$874$	−7832.95			−0.303151
$875$	−9383.06			−0.362520
$876$	−2939.35	+	2939.35i	−0.113369	+	0.113369i
$877$	28443.7	−	28443.7i	1.09518	−	1.09518i	0.100217	−	0.994966i	$-0.468046\pi$
$877$	28443.7	−	28443.7i	1.09518	−	1.09518i	0.994966	−	0.100217i	$-0.0319536\pi$
$878$	16754.9	−	16754.9i	0.644020	−	0.644020i
$879$	12544.4	+	12544.4i	0.481357	+	0.481357i
$880$	5656.48	−	760.752i	0.216682	−	0.0291420i
$881$			42513.6i			1.62579i	0.582410	+	0.812895i	$0.302110\pi$
$881$			42513.6i			1.62579i	−0.582410	+	0.812895i	$0.697890\pi$
$882$	−6410.61	−	6410.61i	−0.244735	−	0.244735i
$883$		−	1045.03i		−	0.0398279i	−0.999802	−	0.0199140i	$-0.993661\pi$
$883$		−	1045.03i		−	0.0398279i	0.999802	−	0.0199140i	$-0.00633923\pi$
$884$	3305.49	−	164.683i	0.125764	−	0.00626571i
$885$	−7329.80			−0.278405
$886$	16771.9	−	16771.9i	0.635962	−	0.635962i
$887$			33154.9i			1.25505i	0.778595	+	0.627527i	$0.215933\pi$
$887$			33154.9i			1.25505i	−0.778595	+	0.627527i	$0.784067\pi$
$888$	5410.82			0.204477
$889$	15868.5	+	15868.5i	0.598662	+	0.598662i
$890$	4472.08	−	4472.08i	0.168432	−	0.168432i
$891$	−751.385	+	984.902i	−0.0282518	+	0.0370319i
$892$	−5291.47	+	5291.47i	−0.198623	+	0.198623i
$893$		−	48799.0i		−	1.82866i
$894$			10767.7i			0.402827i
$895$	−7931.55	+	7931.55i	−0.296226	+	0.296226i
$896$		−	8427.29i		−	0.314214i
$897$	−3636.31	+	181.165i	−0.135354	+	0.00674350i
$898$			8388.87i			0.311738i
$899$	−4678.23	+	4678.23i	−0.173557	+	0.173557i
$900$	−3684.51			−0.136463
$901$	−25829.5			−0.955056
$902$	8451.42	+	6447.61i	0.311975	+	0.238007i
$903$	2583.67	+	2583.67i	0.0952151	+	0.0952151i
$904$	451.960	+	451.960i	0.0166283	+	0.0166283i
$905$	−1040.48	+	1040.48i	−0.0382174	+	0.0382174i
$906$	−12828.0			−0.470401
$907$		−	2256.18i		−	0.0825969i	−0.999147	−	0.0412985i	$-0.986851\pi$
$907$		−	2256.18i		−	0.0825969i	0.999147	−	0.0412985i	$-0.0131494\pi$
$908$	7361.32	+	7361.32i	0.269046	+	0.269046i
$909$	−1647.38			−0.0601102
$910$	3064.26	−	3385.59i	0.111625	−	0.123331i
$911$	4132.00			0.150274			0.0751368	−	0.997173i	$-0.476061\pi$
$911$	4132.00			0.150274			0.0751368	+	0.997173i	$0.476061\pi$
$912$	−12752.1	+	12752.1i	−0.463009	+	0.463009i
$913$	−3127.31	−	23252.7i	−0.113361	−	0.842882i
$914$		−	27215.4i		−	0.984908i
$915$	−963.831	+	963.831i	−0.0348232	+	0.0348232i
$916$	5221.81	+	5221.81i	0.188355	+	0.188355i
$917$	18189.1	−	18189.1i	0.655023	−	0.655023i
$918$	−9026.58	+	9026.58i	−0.324533	+	0.324533i
$919$			4164.53i			0.149483i	0.997203	+	0.0747417i	$0.0238132\pi$
$919$			4164.53i			0.149483i	−0.997203	+	0.0747417i	$0.976187\pi$
$920$	−2098.87			−0.0752148
$921$	8438.74	+	8438.74i	0.301918	+	0.301918i
$922$		−	20501.7i		−	0.732309i
$923$	−25249.9	+	27897.8i	−0.900444	+	0.994871i
$924$	327.622	+	2435.99i	0.0116645	+	0.0867296i
$925$	−5666.22	−	5666.22i	−0.201410	−	0.201410i
$926$			685.425i			0.0243245i
$927$		−	10121.7i		−	0.358619i
$928$	−4565.46	−	4565.46i	−0.161496	−	0.161496i
$929$	−17947.2	−	17947.2i	−0.633830	−	0.633830i	0.315196	−	0.949027i	$-0.397930\pi$
$929$	−17947.2	−	17947.2i	−0.633830	−	0.633830i	−0.949027	+	0.315196i	$0.897930\pi$
$930$	1613.82	+	1613.82i	0.0569023	+	0.0569023i
$931$	−19162.5	−	19162.5i	−0.674571	−	0.674571i
$932$		−	2634.40i		−	0.0925887i
$933$		−	4481.92i		−	0.157269i
$934$	3702.61	+	3702.61i	0.129714	+	0.129714i
$935$	4664.74	−	627.372i	0.163159	−	0.0219436i
$936$	13259.4	−	14649.8i	0.463030	−	0.511586i
$937$		−	4268.23i		−	0.148812i	−0.997228	−	0.0744061i	$-0.976294\pi$
$937$		−	4268.23i		−	0.148812i	0.997228	−	0.0744061i	$-0.0237061\pi$
$938$	−2724.43	−	2724.43i	−0.0948355	−	0.0948355i
$939$	6177.22			0.214682
$940$		−	2498.29i		−	0.0866864i
$941$	5854.38	−	5854.38i	0.202813	−	0.202813i	−0.598391	−	0.801204i	$-0.704193\pi$
$941$	5854.38	−	5854.38i	0.202813	−	0.202813i	0.801204	+	0.598391i	$0.204193\pi$
$942$	−7730.45	+	7730.45i	−0.267380	+	0.267380i
$943$	−2072.75	−	2072.75i	−0.0715779	−	0.0715779i
$944$	−21779.9	+	21779.9i	−0.750929	+	0.750929i
$945$		−	5446.37i		−	0.187482i
$946$	1231.83	+	9159.15i	0.0423366	+	0.314788i
$947$	−140.898	+	140.898i	−0.00483480	+	0.00483480i	−0.709520	−	0.704685i	$-0.751088\pi$
$947$	−140.898	+	140.898i	−0.00483480	+	0.00483480i	0.704685	+	0.709520i	$0.251088\pi$
$948$	−5209.95			−0.178493
$949$	−22154.1	+	24477.4i	−0.757802	+	0.837270i
$950$	35617.4			1.21640
$951$	−979.254	−	979.254i	−0.0333906	−	0.0333906i
$952$		−	10428.6i		−	0.355034i
$953$	46413.9			1.57764			0.788821	−	0.614623i	$-0.210692\pi$
$953$	46413.9			1.57764			0.788821	+	0.614623i	$0.210692\pi$
$954$	−20833.9	+	20833.9i	−0.707046	+	0.707046i
$955$	−2356.32	−	2356.32i	−0.0798415	−	0.0798415i
$956$	−1219.49	−	1219.49i	−0.0412564	−	0.0412564i
$957$	−7000.53	−	5340.73i	−0.236463	−	0.180398i
$958$	−18698.8			−0.630616
$959$	−21480.1			−0.723282
$960$	−4339.03	+	4339.03i	−0.145877	+	0.145877i
$961$		−	22460.0i		−	0.753921i
$962$	8200.38	−	408.551i	0.274835	−	0.0136925i
$963$			25789.5i			0.862985i
$964$	1107.88	−	1107.88i	0.0370151	−	0.0370151i
$965$		−	5576.07i		−	0.186010i
$966$			2191.91i			0.0730058i
$967$	2979.47	−	2979.47i	0.0990831	−	0.0990831i	−0.655828	−	0.754911i	$-0.727680\pi$
$967$	2979.47	−	2979.47i	0.0990831	−	0.0990831i	0.754911	+	0.655828i	$0.227680\pi$
$968$	−16111.5	+	28269.1i	−0.534962	+	0.938639i
$969$	−10516.3	+	10516.3i	−0.348640	+	0.348640i
$970$	9084.89	+	9084.89i	0.300720	+	0.300720i
$971$	40573.9			1.34097			0.670484	−	0.741924i	$-0.266087\pi$
$971$	40573.9			1.34097			0.670484	+	0.741924i	$0.266087\pi$
$972$		−	7250.55i		−	0.239261i
$973$	25293.9	−	25293.9i	0.833386	−	0.833386i
$974$	28008.8			0.921416
$975$	16534.8	−	823.779i	0.543114	−	0.0270585i
$976$			5727.90i			0.187854i
$977$	40895.8	+	40895.8i	1.33917	+	1.33917i	0.896861	+	0.442313i	$0.145842\pi$
$977$	40895.8	+	40895.8i	1.33917	+	1.33917i	0.442313	+	0.896861i	$0.354158\pi$
$978$			16329.6i			0.533910i
$979$	3603.80	+	26795.6i	0.117649	+	0.874761i
$980$	−981.034	−	981.034i	−0.0319775	−	0.0319775i
$981$	5387.04	−	5387.04i	0.175326	−	0.175326i
$982$	17469.8	−	17469.8i	0.567702	−	0.567702i
$983$	13871.9	−	13871.9i	0.450097	−	0.450097i	−0.445290	−	0.895387i	$-0.646899\pi$
$983$	13871.9	−	13871.9i	0.450097	−	0.450097i	0.895387	+	0.445290i	$0.146899\pi$
$984$	−9000.21			−0.291582
$985$	14049.1			0.454459
$986$	5047.22	+	5047.22i	0.163018	+	0.163018i
$987$	−13655.5			−0.440385
$988$	7572.66	−	8366.78i	0.243844	−	0.269416i
$989$		−	2548.43i		−	0.0819368i
$990$	3256.51	−	4268.58i	0.104544	−	0.137035i
$991$	−27611.1			−0.885061			−0.442531	−	0.896753i	$-0.645919\pi$
$991$	−27611.1			−0.885061			−0.442531	+	0.896753i	$0.645919\pi$
$992$	−7154.24			−0.228979
$993$	−13335.7	−	13335.7i	−0.426180	−	0.426180i
$994$	16018.3	+	16018.3i	0.511136	+	0.511136i
$995$	6122.13	−	6122.13i	0.195060	−	0.195060i
$996$	2683.74	+	2683.74i	0.0853790	+	0.0853790i
$997$		−	4628.82i		−	0.147037i	−0.997294	−	0.0735186i	$-0.976577\pi$
$997$		−	4628.82i		−	0.147037i	0.997294	−	0.0735186i	$-0.0234228\pi$
$998$	−14612.7			−0.463485
$999$	6924.55	−	6924.55i	0.219302	−	0.219302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.13	✓	80
11.10	odd	2	inner	143.4.g.a.21.28	yes	80
13.5	odd	4	inner	143.4.g.a.109.28	yes	80
143.109	even	4	inner	143.4.g.a.109.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.13	✓	80	1.1	even	1	trivial
143.4.g.a.21.28	yes	80	11.10	odd	2	inner
143.4.g.a.109.13	yes	80	143.109	even	4	inner
143.4.g.a.109.28	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)

\(f(q)\)	\(=\)	\(q+(-1.74793 + 1.74793i) q^{2} -3.12343 q^{3} +1.88950i q^{4} +(-2.44120 - 2.44120i) q^{5} +(5.45953 - 5.45953i) q^{6} +(8.07208 + 8.07208i) q^{7} +(-17.2861 - 17.2861i) q^{8} -17.2442 q^{9} +O(q^{10})\)	\(q+(-1.74793 + 1.74793i) q^{2} -3.12343 q^{3} +1.88950i q^{4} +(-2.44120 - 2.44120i) q^{5} +(5.45953 - 5.45953i) q^{6} +(8.07208 + 8.07208i) q^{7} +(-17.2861 - 17.2861i) q^{8} -17.2442 q^{9} +8.53410 q^{10} +(-22.1285 + 29.0057i) q^{11} -5.90172i q^{12} +(-2.33233 - 46.8141i) q^{13} -28.2188 q^{14} +(7.62493 + 7.62493i) q^{15} +45.3138 q^{16} +37.3690 q^{17} +(30.1416 - 30.1416i) q^{18} +(90.0989 - 90.0989i) q^{19} +(4.61266 - 4.61266i) q^{20} +(-25.2126 - 25.2126i) q^{21} +(-12.0208 - 89.3788i) q^{22} +24.8687i q^{23} +(53.9920 + 53.9920i) q^{24} -113.081i q^{25} +(85.9044 + 77.7509i) q^{26} +138.194 q^{27} +(-15.2522 + 15.2522i) q^{28} -77.2710i q^{29} -26.6556 q^{30} +(-60.5432 - 60.5432i) q^{31} +(59.0838 - 59.0838i) q^{32} +(69.1168 - 90.5971i) q^{33} +(-65.3184 + 65.3184i) q^{34} -39.4112i q^{35} -32.5829i q^{36} +(50.1076 - 50.1076i) q^{37} +314.973i q^{38} +(7.28486 + 146.221i) q^{39} +84.3980i q^{40} +(-83.3477 + 83.3477i) q^{41} +88.1394 q^{42} -102.476 q^{43} +(-54.8062 - 41.8118i) q^{44} +(42.0966 + 42.0966i) q^{45} +(-43.4687 - 43.4687i) q^{46} +(270.808 - 270.808i) q^{47} -141.534 q^{48} -212.683i q^{49} +(197.657 + 197.657i) q^{50} -116.720 q^{51} +(88.4552 - 4.40693i) q^{52} -691.201 q^{53} +(-241.552 + 241.552i) q^{54} +(124.829 - 16.7885i) q^{55} -279.070i q^{56} +(-281.417 + 281.417i) q^{57} +(135.064 + 135.064i) q^{58} +(-480.647 + 480.647i) q^{59} +(-14.4073 + 14.4073i) q^{60} +126.405i q^{61} +211.650 q^{62} +(-139.196 - 139.196i) q^{63} +569.059i q^{64} +(-108.589 + 119.977i) q^{65} +(37.5460 + 279.168i) q^{66} +(96.5465 + 96.5465i) q^{67} +70.6088i q^{68} -77.6756i q^{69} +(68.8879 + 68.8879i) q^{70} +(-567.646 - 567.646i) q^{71} +(298.085 + 298.085i) q^{72} +(-498.050 - 498.050i) q^{73} +175.169i q^{74} +353.201i q^{75} +(170.242 + 170.242i) q^{76} +(-412.759 + 55.5129i) q^{77} +(-268.316 - 242.849i) q^{78} -882.786i q^{79} +(-110.620 - 110.620i) q^{80} +33.9555 q^{81} -291.371i q^{82} +(-454.739 + 454.739i) q^{83} +(47.6391 - 47.6391i) q^{84} +(-91.2255 - 91.2255i) q^{85} +(179.120 - 179.120i) q^{86} +241.350i q^{87} +(883.912 - 118.879i) q^{88} +(524.025 - 524.025i) q^{89} -147.164 q^{90} +(359.060 - 396.714i) q^{91} -46.9894 q^{92} +(189.102 + 189.102i) q^{93} +946.706i q^{94} -439.900 q^{95} +(-184.544 + 184.544i) q^{96} +(1064.54 + 1064.54i) q^{97} +(371.755 + 371.755i) q^{98} +(381.588 - 500.179i) 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

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Database

Properties

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