LMFDB - Embedded newform 143.4.g.a.21.14

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			21.14
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57816 + 1.57816i) q^{2} -8.34617 q^{3} +3.01884i q^{4} +(-13.3430 - 13.3430i) q^{5} +(13.1716 - 13.1716i) q^{6} +(-5.61955 - 5.61955i) q^{7} +(-17.3895 - 17.3895i) q^{8} +42.6586 q^{9} +O(q^{10})$	\(q+(-1.57816 + 1.57816i) q^{2} -8.34617 q^{3} +3.01884i q^{4} +(-13.3430 - 13.3430i) q^{5} +(13.1716 - 13.1716i) q^{6} +(-5.61955 - 5.61955i) q^{7} +(-17.3895 - 17.3895i) q^{8} +42.6586 q^{9} +42.1147 q^{10} +(-33.5062 - 14.4338i) q^{11} -25.1958i q^{12} +(3.73989 + 46.7227i) q^{13} +17.7371 q^{14} +(111.363 + 111.363i) q^{15} +30.7359 q^{16} -120.961 q^{17} +(-67.3220 + 67.3220i) q^{18} +(30.7000 - 30.7000i) q^{19} +(40.2804 - 40.2804i) q^{20} +(46.9018 + 46.9018i) q^{21} +(75.6568 - 30.0992i) q^{22} +108.069i q^{23} +(145.135 + 145.135i) q^{24} +231.071i q^{25} +(-79.6379 - 67.8337i) q^{26} -130.690 q^{27} +(16.9645 - 16.9645i) q^{28} -50.1406i q^{29} -351.496 q^{30} +(53.9186 + 53.9186i) q^{31} +(90.6097 - 90.6097i) q^{32} +(279.649 + 120.467i) q^{33} +(190.896 - 190.896i) q^{34} +149.963i q^{35} +128.780i q^{36} +(199.880 - 199.880i) q^{37} +96.8989i q^{38} +(-31.2138 - 389.956i) q^{39} +464.055i q^{40} +(111.123 - 111.123i) q^{41} -148.037 q^{42} -163.931 q^{43} +(43.5734 - 101.150i) q^{44} +(-569.194 - 569.194i) q^{45} +(-170.550 - 170.550i) q^{46} +(-363.252 + 363.252i) q^{47} -256.527 q^{48} -279.841i q^{49} +(-364.666 - 364.666i) q^{50} +1009.57 q^{51} +(-141.048 + 11.2901i) q^{52} -18.5606 q^{53} +(206.249 - 206.249i) q^{54} +(254.483 + 639.663i) q^{55} +195.442i q^{56} +(-256.228 + 256.228i) q^{57} +(79.1297 + 79.1297i) q^{58} +(350.097 - 350.097i) q^{59} +(-336.187 + 336.187i) q^{60} -540.958i q^{61} -170.184 q^{62} +(-239.722 - 239.722i) q^{63} +531.879i q^{64} +(573.519 - 673.322i) q^{65} +(-631.445 + 251.213i) q^{66} +(369.368 + 369.368i) q^{67} -365.163i q^{68} -901.964i q^{69} +(-236.666 - 236.666i) q^{70} +(495.232 + 495.232i) q^{71} +(-741.811 - 741.811i) q^{72} +(-823.253 - 823.253i) q^{73} +630.884i q^{74} -1928.56i q^{75} +(92.6785 + 92.6785i) q^{76} +(107.178 + 269.401i) q^{77} +(664.672 + 566.152i) q^{78} +780.706i q^{79} +(-410.108 - 410.108i) q^{80} -61.0243 q^{81} +350.738i q^{82} +(-82.9443 + 82.9443i) q^{83} +(-141.589 + 141.589i) q^{84} +(1613.99 + 1613.99i) q^{85} +(258.709 - 258.709i) q^{86} +418.482i q^{87} +(331.659 + 833.651i) q^{88} +(80.9085 - 80.9085i) q^{89} +1796.55 q^{90} +(241.544 - 283.577i) q^{91} -326.244 q^{92} +(-450.014 - 450.014i) q^{93} -1146.54i q^{94} -819.260 q^{95} +(-756.244 + 756.244i) q^{96} +(104.137 + 104.137i) q^{97} +(441.633 + 441.633i) q^{98} +(-1429.33 - 615.726i) 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 $

$2$	−1.57816	+	1.57816i	−0.557963	+	0.557963i	−0.928727	−	0.370764i	$-0.879096\pi$
$2$	−1.57816	+	1.57816i	−0.557963	+	0.557963i	0.370764	+	0.928727i	$0.379096\pi$
$3$	−8.34617			−1.60622			−0.803111	−	0.595829i	$-0.796823\pi$
$3$	−8.34617			−1.60622			−0.803111	+	0.595829i	$0.796823\pi$
$4$			3.01884i			0.377355i
$5$	−13.3430	−	13.3430i	−1.19343	−	1.19343i	−0.976097	−	0.217336i	$-0.930263\pi$
$5$	−13.3430	−	13.3430i	−1.19343	−	1.19343i	−0.217336	−	0.976097i	$-0.569737\pi$
$6$	13.1716	−	13.1716i	0.896212	−	0.896212i
$7$	−5.61955	−	5.61955i	−0.303427	−	0.303427i	0.538926	−	0.842353i	$-0.318830\pi$
$7$	−5.61955	−	5.61955i	−0.303427	−	0.303427i	−0.842353	+	0.538926i	$0.818830\pi$
$8$	−17.3895	−	17.3895i	−0.768513	−	0.768513i
$9$	42.6586			1.57995
$10$	42.1147			1.33178
$11$	−33.5062	−	14.4338i	−0.918409	−	0.395632i
$11$	−33.5062	−	14.4338i	−0.918409	−	0.395632i
$12$		−	25.1958i		−	0.606116i
$13$	3.73989	+	46.7227i	0.0797892	+	0.996812i
$13$	3.73989	+	46.7227i	0.0797892	+	0.996812i
$14$	17.7371			0.338602
$15$	111.363	+	111.363i	1.91692	+	1.91692i
$16$	30.7359			0.480248
$17$	−120.961			−1.72573			−0.862866	−	0.505432i	$-0.831333\pi$
$17$	−120.961			−1.72573			−0.862866	+	0.505432i	$0.831333\pi$
$18$	−67.3220	+	67.3220i	−0.881553	+	0.881553i
$19$	30.7000	−	30.7000i	0.370688	−	0.370688i	−0.497040	−	0.867728i	$-0.665580\pi$
$19$	30.7000	−	30.7000i	0.370688	−	0.370688i	0.867728	+	0.497040i	$0.165580\pi$
$20$	40.2804	−	40.2804i	0.450348	−	0.450348i
$21$	46.9018	+	46.9018i	0.487372	+	0.487372i
$22$	75.6568	−	30.0992i	0.733186	−	0.291690i
$23$			108.069i			0.979738i	0.871796	+	0.489869i	$0.162955\pi$
$23$			108.069i			0.979738i	−0.871796	+	0.489869i	$0.837045\pi$
$24$	145.135	+	145.135i	1.23440	+	1.23440i
$25$			231.071i			1.84856i
$26$	−79.6379	−	67.8337i	−0.600703	−	0.511664i
$27$	−130.690			−0.931527
$28$	16.9645	−	16.9645i	0.114500	−	0.114500i
$29$		−	50.1406i		−	0.321064i	−0.987031	−	0.160532i	$-0.948679\pi$
$29$		−	50.1406i		−	0.321064i	0.987031	−	0.160532i	$-0.0513211\pi$
$30$	−351.496			−2.13914
$31$	53.9186	+	53.9186i	0.312389	+	0.312389i	0.845835	−	0.533445i	$-0.179103\pi$
$31$	53.9186	+	53.9186i	0.312389	+	0.312389i	−0.533445	+	0.845835i	$0.679103\pi$
$32$	90.6097	−	90.6097i	0.500552	−	0.500552i
$33$	279.649	+	120.467i	1.47517	+	0.635473i
$34$	190.896	−	190.896i	0.962895	−	0.962895i
$35$			149.963i			0.724240i
$36$			128.780i			0.596202i
$37$	199.880	−	199.880i	0.888110	−	0.888110i	−0.106232	−	0.994341i	$-0.533879\pi$
$37$	199.880	−	199.880i	0.888110	−	0.888110i	0.994341	+	0.106232i	$0.0338785\pi$
$38$			96.8989i			0.413660i
$39$	−31.2138	−	389.956i	−0.128159	−	1.60110i
$40$			464.055i			1.83434i
$41$	111.123	−	111.123i	0.423280	−	0.423280i	−0.463052	−	0.886331i	$-0.653246\pi$
$41$	111.123	−	111.123i	0.423280	−	0.423280i	0.886331	+	0.463052i	$0.153246\pi$
$42$	−148.037			−0.543870
$43$	−163.931			−0.581379			−0.290689	−	0.956817i	$-0.593885\pi$
$43$	−163.931			−0.581379			−0.290689	+	0.956817i	$0.593885\pi$
$44$	43.5734	−	101.150i	0.149294	−	0.346566i
$45$	−569.194	−	569.194i	−1.88556	−	1.88556i
$46$	−170.550	−	170.550i	−0.546658	−	0.546658i
$47$	−363.252	+	363.252i	−1.12736	+	1.12736i	−0.136751	+	0.990605i	$0.543666\pi$
$47$	−363.252	+	363.252i	−1.12736	+	1.12736i	−0.990605	+	0.136751i	$0.956334\pi$
$48$	−256.527			−0.771385
$49$		−	279.841i		−	0.815864i
$50$	−364.666	−	364.666i	−1.03143	−	1.03143i
$51$	1009.57			2.77191
$52$	−141.048	+	11.2901i	−0.376152	+	0.0301089i
$53$	−18.5606			−0.0481037			−0.0240519	−	0.999711i	$-0.507657\pi$
$53$	−18.5606			−0.0481037			−0.0240519	+	0.999711i	$0.507657\pi$
$54$	206.249	−	206.249i	0.519758	−	0.519758i
$55$	254.483	+	639.663i	0.623899	+	1.56822i
$56$			195.442i			0.466376i
$57$	−256.228	+	256.228i	−0.595407	+	0.595407i
$58$	79.1297	+	79.1297i	0.179142	+	0.179142i
$59$	350.097	−	350.097i	0.772522	−	0.772522i	−0.206025	−	0.978547i	$-0.566053\pi$
$59$	350.097	−	350.097i	0.772522	−	0.772522i	0.978547	+	0.206025i	$0.0660528\pi$
$60$	−336.187	+	336.187i	−0.723359	+	0.723359i
$61$		−	540.958i		−	1.13545i	−0.823218	−	0.567726i	$-0.807823\pi$
$61$		−	540.958i		−	1.13545i	0.823218	−	0.567726i	$-0.192177\pi$
$62$	−170.184			−0.348603
$63$	−239.722	−	239.722i	−0.479400	−	0.479400i
$64$			531.879i			1.03883i
$65$	573.519	−	673.322i	1.09440	−	1.28485i
$66$	−631.445	+	251.213i	−1.17766	+	0.468519i
$67$	369.368	+	369.368i	0.673514	+	0.673514i	0.958524	−	0.285010i	$-0.0919970\pi$
$67$	369.368	+	369.368i	0.673514	+	0.673514i	−0.285010	+	0.958524i	$0.591997\pi$
$68$		−	365.163i		−	0.651214i
$69$		−	901.964i		−	1.57368i
$70$	−236.666	−	236.666i	−0.404099	−	0.404099i
$71$	495.232	+	495.232i	0.827792	+	0.827792i	0.987211	−	0.159419i	$-0.0509620\pi$
$71$	495.232	+	495.232i	0.827792	+	0.827792i	−0.159419	+	0.987211i	$0.550962\pi$
$72$	−741.811	−	741.811i	−1.21421	−	1.21421i
$73$	−823.253	−	823.253i	−1.31992	−	1.31992i	−0.913832	−	0.406093i	$-0.866891\pi$
$73$	−823.253	−	823.253i	−1.31992	−	1.31992i	−0.406093	−	0.913832i	$-0.633109\pi$
$74$			630.884i			0.991064i
$75$		−	1928.56i		−	2.96921i
$76$	92.6785	+	92.6785i	0.139881	+	0.139881i
$77$	107.178	+	269.401i	0.158625	+	0.398716i
$78$	664.672	+	566.152i	0.964863	+	0.821847i
$79$			780.706i			1.11185i	0.831232	+	0.555926i	$0.187636\pi$
$79$			780.706i			1.11185i	−0.831232	+	0.555926i	$0.812364\pi$
$80$	−410.108	−	410.108i	−0.573144	−	0.573144i
$81$	−61.0243			−0.0837096
$82$			350.738i			0.472349i
$83$	−82.9443	+	82.9443i	−0.109691	+	0.109691i	−0.759822	−	0.650131i	$-0.774714\pi$
$83$	−82.9443	+	82.9443i	−0.109691	+	0.109691i	0.650131	+	0.759822i	$0.274714\pi$
$84$	−141.589	+	141.589i	−0.183912	+	0.183912i
$85$	1613.99	+	1613.99i	2.05955	+	2.05955i
$86$	258.709	−	258.709i	0.324388	−	0.324388i
$87$			418.482i			0.515701i
$88$	331.659	+	833.651i	0.401761	+	1.00986i
$89$	80.9085	−	80.9085i	0.0963628	−	0.0963628i	−0.657282	−	0.753645i	$-0.728294\pi$
$89$	80.9085	−	80.9085i	0.0963628	−	0.0963628i	0.753645	+	0.657282i	$0.228294\pi$
$90$	1796.55			2.10415
$91$	241.544	−	283.577i	0.278250	−	0.326670i
$92$	−326.244			−0.369709
$93$	−450.014	−	450.014i	−0.501766	−	0.501766i
$94$		−	1146.54i		−	1.25805i
$95$	−819.260			−0.884782
$96$	−756.244	+	756.244i	−0.803998	+	0.803998i
$97$	104.137	+	104.137i	0.109005	+	0.109005i	0.759506	−	0.650501i	$-0.225441\pi$
$97$	104.137	+	104.137i	0.109005	+	0.109005i	−0.650501	+	0.759506i	$0.725441\pi$
$98$	441.633	+	441.633i	0.455222	+	0.455222i
$99$	−1429.33	−	615.726i	−1.45104	−	0.625079i
$100$	−697.565			−0.697565
$101$	262.603			0.258713			0.129356	−	0.991598i	$-0.458709\pi$
$101$	262.603			0.258713			0.129356	+	0.991598i	$0.458709\pi$
$102$	−1593.25	+	1593.25i	−1.54662	+	1.54662i
$103$			229.093i			0.219158i	0.993978	+	0.109579i	$0.0349502\pi$
$103$			229.093i			0.219158i	−0.993978	+	0.109579i	$0.965050\pi$
$104$	747.448	−	877.518i	0.704744	−	0.827382i
$105$		−	1251.62i		−	1.16329i
$106$	29.2916	−	29.2916i	0.0268401	−	0.0268401i
$107$		−	82.9522i		−	0.0749466i	−0.999298	−	0.0374733i	$-0.988069\pi$
$107$		−	82.9522i		−	0.0749466i	0.999298	−	0.0374733i	$-0.0119309\pi$
$108$		−	394.531i		−	0.351517i
$109$	−1263.25	+	1263.25i	−1.11007	+	1.11007i	−0.116932	+	0.993140i	$0.537306\pi$
$109$	−1263.25	+	1263.25i	−1.11007	+	1.11007i	−0.993140	+	0.116932i	$0.962694\pi$
$110$	−1411.10	−	607.875i	−1.22312	−	0.526896i
$111$	−1668.23	+	1668.23i	−1.42650	+	1.42650i
$112$	−172.722	−	172.722i	−0.145720	−	0.145720i
$113$	869.922			0.724207			0.362104	−	0.932138i	$-0.382059\pi$
$113$	869.922			0.724207			0.362104	+	0.932138i	$0.382059\pi$
$114$		−	808.735i		−	0.664430i
$115$	1441.97	−	1441.97i	1.16925	−	1.16925i
$116$	151.366			0.121155
$117$	159.539	+	1993.13i	0.126063	+	1.57491i
$118$			1105.02i			0.862077i
$119$	679.749	+	679.749i	0.523635	+	0.523635i
$120$		−	3873.08i		−	2.94635i
$121$	914.331	+	967.244i	0.686950	+	0.726705i
$122$	853.716	+	853.716i	0.633540	+	0.633540i
$123$	−927.450	+	927.450i	−0.679881	+	0.679881i
$124$	−162.772	+	162.772i	−0.117882	+	0.117882i
$125$	1415.30	−	1415.30i	1.01271	−	1.01271i
$126$	756.639			0.534974
$127$	801.042			0.559693			0.279846	−	0.960045i	$-0.409716\pi$
$127$	801.042			0.559693			0.279846	+	0.960045i	$0.409716\pi$
$128$	−114.512	−	114.512i	−0.0790745	−	0.0790745i
$129$	1368.20			0.933823
$130$	157.504	+	1967.71i	0.106262	+	1.32754i
$131$		−	270.563i		−	0.180452i	−0.995921	−	0.0902258i	$-0.971241\pi$
$131$		−	270.563i		−	0.180452i	0.995921	−	0.0902258i	$-0.0287589\pi$
$132$	−363.671	+	844.215i	−0.239799	+	0.556663i
$133$	−345.041			−0.224954
$134$	−1165.84			−0.751592
$135$	1743.79	+	1743.79i	1.11172	+	1.11172i
$136$	2103.45	+	2103.45i	1.32625	+	1.32625i
$137$	−795.869	+	795.869i	−0.496319	+	0.496319i	−0.910290	−	0.413971i	$-0.864141\pi$
$137$	−795.869	+	795.869i	−0.496319	+	0.496319i	0.413971	+	0.910290i	$0.364141\pi$
$138$	1423.44	+	1423.44i	0.878053	+	0.878053i
$139$			906.443i			0.553118i	0.960997	+	0.276559i	$0.0891942\pi$
$139$			906.443i			0.553118i	−0.960997	+	0.276559i	$0.910806\pi$
$140$	−452.715			−0.273296
$141$	3031.76	−	3031.76i	1.81078	−	1.81078i
$142$	−1563.11			−0.923755
$143$	549.077	−	1619.48i	0.321092	−	0.947048i
$144$	1311.15			0.758767
$145$	−669.025	+	669.025i	−0.383169	+	0.383169i
$146$	2598.45			1.47294
$147$			2335.60i			1.31046i
$148$	603.406	+	603.406i	0.335133	+	0.335133i
$149$	1370.06	−	1370.06i	0.753285	−	0.753285i	−0.221806	−	0.975091i	$-0.571195\pi$
$149$	1370.06	−	1370.06i	0.753285	−	0.753285i	0.975091	+	0.221806i	$0.0711951\pi$
$150$	3043.56	+	3043.56i	1.65671	+	1.65671i
$151$	391.816	+	391.816i	0.211163	+	0.211163i	0.804761	−	0.593599i	$-0.202293\pi$
$151$	391.816	+	391.816i	0.211163	+	0.211163i	−0.593599	+	0.804761i	$0.702293\pi$
$152$	−1067.71			−0.569757
$153$	−5160.05			−2.72657
$154$	−594.302	−	256.013i	−0.310975	−	0.133962i
$155$		−	1438.87i		−	0.745631i
$156$	1177.22	−	94.2295i	0.604184	−	0.0483615i
$157$	−3365.26			−1.71068			−0.855341	−	0.518065i	$-0.826652\pi$
$157$	−3365.26			−1.71068			−0.855341	+	0.518065i	$0.826652\pi$
$158$	−1232.08	−	1232.08i	−0.620372	−	0.620372i
$159$	154.910			0.0772652
$160$	−2418.01			−1.19475
$161$	607.301	−	607.301i	0.297279	−	0.297279i
$162$	96.3059	−	96.3059i	0.0467068	−	0.0467068i
$163$	1727.22	−	1727.22i	0.829976	−	0.829976i	−0.157537	−	0.987513i	$-0.550355\pi$
$163$	1727.22	−	1727.22i	0.829976	−	0.829976i	0.987513	+	0.157537i	$0.0503554\pi$
$164$	335.462	+	335.462i	0.159727	+	0.159727i
$165$	−2123.96	−	5338.74i	−1.00212	−	2.51891i
$166$		−	261.798i		−	0.122407i
$167$	−2612.33	−	2612.33i	−1.21047	−	1.21047i	−0.970873	−	0.239596i	$-0.922985\pi$
$167$	−2612.33	−	2612.33i	−1.21047	−	1.21047i	−0.239596	−	0.970873i	$-0.577015\pi$
$168$		−	1631.19i		−	0.749103i
$169$	−2169.03	+	349.476i	−0.987267	+	0.159070i
$170$	−5094.25			−2.29830
$171$	1309.62	−	1309.62i	0.585668	−	0.585668i
$172$		−	494.883i		−	0.219386i
$173$	4256.32			1.87053			0.935267	−	0.353944i	$-0.115160\pi$
$173$	4256.32			1.87053			0.935267	+	0.353944i	$0.115160\pi$
$174$	−660.430	−	660.430i	−0.287742	−	0.287742i
$175$	1298.51	−	1298.51i	0.560905	−	0.560905i
$176$	−1029.84	−	443.635i	−0.441064	−	0.190002i
$177$	−2921.97	+	2921.97i	−1.24084	+	1.24084i
$178$			255.373i			0.107534i
$179$			3579.81i			1.49479i	0.664380	+	0.747395i	$0.268696\pi$
$179$			3579.81i			1.49479i	−0.664380	+	0.747395i	$0.731304\pi$
$180$	1718.30	−	1718.30i	0.711527	−	0.711527i
$181$		−	1635.03i		−	0.671441i	−0.941962	−	0.335720i	$-0.891020\pi$
$181$		−	1635.03i		−	0.671441i	0.941962	−	0.335720i	$-0.108980\pi$
$182$	66.3348	+	828.724i	0.0270168	+	0.337523i
$183$			4514.93i			1.82379i
$184$	1879.26	−	1879.26i	0.752942	−	0.752942i
$185$	−5333.99			−2.11980
$186$	1420.39			0.559934
$187$	4052.96	+	1745.93i	1.58493	+	0.682756i
$188$	−1096.60	−	1096.60i	−0.425414	−	0.425414i
$189$	734.417	+	734.417i	0.282651	+	0.282651i
$190$	1292.92	−	1292.92i	0.493676	−	0.493676i
$191$	−1315.97			−0.498537			−0.249269	−	0.968434i	$-0.580190\pi$
$191$	−1315.97			−0.498537			−0.249269	+	0.968434i	$0.580190\pi$
$192$		−	4439.16i		−	1.66859i
$193$	−2067.18	−	2067.18i	−0.770977	−	0.770977i	0.207300	−	0.978277i	$-0.433532\pi$
$193$	−2067.18	−	2067.18i	−0.770977	−	0.770977i	−0.978277	+	0.207300i	$0.933532\pi$
$194$	−328.689			−0.121642
$195$	−4786.69	+	5619.66i	−1.75786	+	2.06376i
$196$	844.796			0.307870
$197$	−1003.51	+	1003.51i	−0.362928	+	0.362928i	−0.864890	−	0.501962i	$-0.832612\pi$
$197$	−1003.51	+	1003.51i	−0.362928	+	0.362928i	0.501962	+	0.864890i	$0.332612\pi$
$198$	3227.42	−	1283.99i	1.15840	−	0.460855i
$199$		−	4306.50i		−	1.53407i	−0.641606	−	0.767035i	$-0.721731\pi$
$199$		−	4306.50i		−	1.53407i	0.641606	−	0.767035i	$-0.278269\pi$
$200$	4018.19	−	4018.19i	1.42065	−	1.42065i
$201$	−3082.81	−	3082.81i	−1.08181	−	1.08181i
$202$	−414.429	+	414.429i	−0.144352	+	0.144352i
$203$	−281.768	+	281.768i	−0.0974197	+	0.0974197i
$204$			3047.72i			1.04599i
$205$	−2965.42			−1.01031
$206$	−361.545	−	361.545i	−0.122282	−	0.122282i
$207$			4610.08i			1.54794i
$208$	114.949	+	1436.06i	0.0383186	+	0.478717i
$209$	−1471.76	+	585.523i	−0.487099	+	0.193787i
$210$	1975.25	+	1975.25i	0.649073	+	0.649073i
$211$		−	413.866i		−	0.135032i	−0.997718	−	0.0675159i	$-0.978493\pi$
$211$		−	413.866i		−	0.135032i	0.997718	−	0.0675159i	$-0.0215073\pi$
$212$		−	56.0315i		−	0.0181522i
$213$	−4133.30	−	4133.30i	−1.32962	−	1.32962i
$214$	130.912	+	130.912i	0.0418174	+	0.0418174i
$215$	2187.33	+	2187.33i	0.693837	+	0.693837i
$216$	2272.62	+	2272.62i	0.715891	+	0.715891i
$217$		−	605.997i		−	0.189575i
$218$		−	3987.23i		−	1.23876i
$219$	6871.02	+	6871.02i	2.12009	+	2.12009i
$220$	−1931.04	+	768.243i	−0.591776	+	0.235431i
$221$	−452.383	−	5651.65i	−0.137695	−	1.72023i
$222$		−	5265.47i		−	1.59187i
$223$	2495.36	+	2495.36i	0.749336	+	0.749336i	0.974355	−	0.225018i	$-0.0722442\pi$
$223$	2495.36	+	2495.36i	0.749336	+	0.749336i	−0.225018	+	0.974355i	$0.572244\pi$
$224$	−1018.37			−0.303763
$225$			9857.15i			2.92064i
$226$	−1372.87	+	1372.87i	−0.404081	+	0.404081i
$227$	1891.86	−	1891.86i	0.553159	−	0.553159i	−0.374192	−	0.927351i	$-0.622080\pi$
$227$	1891.86	−	1891.86i	0.553159	−	0.553159i	0.927351	+	0.374192i	$0.122080\pi$
$228$	−773.511	−	773.511i	−0.224680	−	0.224680i
$229$	72.8242	−	72.8242i	0.0210147	−	0.0210147i	−0.696521	−	0.717536i	$-0.745270\pi$
$229$	72.8242	−	72.8242i	0.0210147	−	0.0210147i	0.717536	+	0.696521i	$0.245270\pi$
$230$			4551.30i			1.30480i
$231$	−894.529	−	2248.47i	−0.254787	−	0.640427i
$232$	−871.917	+	871.917i	−0.246742	+	0.246742i
$233$	−3191.99			−0.897485			−0.448743	−	0.893661i	$-0.648128\pi$
$233$	−3191.99			−0.897485			−0.448743	+	0.893661i	$0.648128\pi$
$234$	−3397.25	−	2893.69i	−0.949081	−	0.808404i
$235$	9693.73			2.69085
$236$	1056.89	+	1056.89i	0.291515	+	0.291515i
$237$		−	6515.91i		−	1.78588i
$238$	−2145.50			−0.584337
$239$	105.928	−	105.928i	0.0286692	−	0.0286692i	−0.692627	−	0.721296i	$-0.743547\pi$
$239$	105.928	−	105.928i	0.0286692	−	0.0286692i	0.721296	+	0.692627i	$0.243547\pi$
$240$	3422.84	+	3422.84i	0.920596	+	0.920596i
$241$	2857.19	+	2857.19i	0.763684	+	0.763684i	0.976986	−	0.213302i	$-0.0684219\pi$
$241$	2857.19	+	2857.19i	0.763684	+	0.763684i	−0.213302	+	0.976986i	$0.568422\pi$
$242$	−2969.42	−	83.5052i	−0.788767	−	0.0221815i
$243$	4037.94			1.06598
$244$	1633.07			0.428468
$245$	−3733.92	+	3733.92i	−0.973679	+	0.973679i
$246$		−	2927.32i		−	0.758697i
$247$	1549.20	+	1319.57i	0.399083	+	0.339929i
$248$		−	1875.23i		−	0.480150i
$249$	692.268	−	692.268i	0.176188	−	0.176188i
$250$			4467.13i			1.13010i
$251$			942.726i			0.237069i	0.992950	+	0.118535i	$0.0378196\pi$
$251$			942.726i			0.237069i	−0.992950	+	0.118535i	$0.962180\pi$
$252$	723.684	−	723.684i	0.180904	−	0.180904i
$253$	1559.85	−	3620.99i	0.387616	−	0.899801i
$254$	−1264.17	+	1264.17i	−0.312288	+	0.312288i
$255$	−13470.6	−	13470.6i	−3.30809	−	3.30809i
$256$	−3893.60			−0.950586
$257$			218.873i			0.0531243i	0.999647	+	0.0265622i	$0.00845599\pi$
$257$			218.873i			0.0531243i	−0.999647	+	0.0265622i	$0.991544\pi$
$258$	−2159.23	+	2159.23i	−0.521039	+	0.521039i
$259$	−2246.47			−0.538954
$260$	2032.65	+	1731.36i	0.484845	+	0.412979i
$261$		−	2138.93i		−	0.507266i
$262$	426.990	+	426.990i	0.100685	+	0.100685i
$263$			5280.40i			1.23804i	0.785377	+	0.619018i	$0.212469\pi$
$263$			5280.40i			1.23804i	−0.785377	+	0.619018i	$0.787531\pi$
$264$	−2768.08	−	6957.79i	−0.645317	−	1.62206i
$265$	247.654	+	247.654i	0.0574086	+	0.0574086i
$266$	544.529	−	544.529i	0.125516	−	0.125516i
$267$	−675.277	+	675.277i	−0.154780	+	0.154780i
$268$	−1115.06	+	1115.06i	−0.254154	+	0.254154i
$269$	3845.65			0.871648			0.435824	−	0.900032i	$-0.356457\pi$
$269$	3845.65			0.871648			0.435824	+	0.900032i	$0.356457\pi$
$270$	−5503.95			−1.24059
$271$	4119.51	+	4119.51i	0.923405	+	0.923405i	0.997268	−	0.0738638i	$-0.0235330\pi$
$271$	4119.51	+	4119.51i	0.923405	+	0.923405i	−0.0738638	+	0.997268i	$0.523533\pi$
$272$	−3717.86			−0.828780
$273$	−2015.97	+	2366.79i	−0.446931	+	0.524705i
$274$		−	2512.01i		−	0.553855i
$275$	3335.23	−	7742.30i	0.731352	−	1.69774i
$276$	2722.89			0.593835
$277$	6329.13			1.37285			0.686427	−	0.727199i	$-0.259178\pi$
$277$	6329.13			1.37285			0.686427	+	0.727199i	$0.259178\pi$
$278$	−1430.51	−	1430.51i	−0.308619	−	0.308619i
$279$	2300.09	+	2300.09i	0.493559	+	0.493559i
$280$	2607.78	−	2607.78i	0.556588	−	0.556588i
$281$	2370.40	+	2370.40i	0.503225	+	0.503225i	0.912439	−	0.409214i	$-0.134197\pi$
$281$	2370.40	+	2370.40i	0.503225	+	0.503225i	−0.409214	+	0.912439i	$0.634197\pi$
$282$			9569.20i			2.02070i
$283$	−233.611			−0.0490698			−0.0245349	−	0.999699i	$-0.507810\pi$
$283$	−233.611			−0.0490698			−0.0245349	+	0.999699i	$0.507810\pi$
$284$	−1495.03	+	1495.03i	−0.312372	+	0.312372i
$285$	6837.69			1.42116
$286$	1689.27	+	3422.33i	0.349260	+	0.707575i
$287$	−1248.92			−0.256869
$288$	3865.28	−	3865.28i	0.790847	−	0.790847i
$289$	9718.67			1.97815
$290$		−	2111.65i		−	0.427588i
$291$	−869.144	−	869.144i	−0.175086	−	0.175086i
$292$	2485.27	−	2485.27i	0.498080	−	0.498080i
$293$	−1266.46	−	1266.46i	−0.252516	−	0.252516i	0.569485	−	0.822002i	$-0.307143\pi$
$293$	−1266.46	−	1266.46i	−0.252516	−	0.252516i	−0.822002	+	0.569485i	$0.807143\pi$
$294$	−3685.95	−	3685.95i	−0.731187	−	0.731187i
$295$	−9342.69			−1.84391
$296$	−6951.61			−1.36505
$297$	4378.91	+	1886.35i	0.855523	+	0.368542i
$298$			4324.33i			0.840610i
$299$	−5049.29	+	404.167i	−0.976615	+	0.0781726i
$300$	5822.00			1.12044
$301$	921.221	+	921.221i	0.176406	+	0.176406i
$302$	−1236.69			−0.235642
$303$	−2191.73			−0.415550
$304$	943.592	−	943.592i	0.178022	−	0.178022i
$305$	−7217.99	+	7217.99i	−1.35509	+	1.35509i
$306$	8143.37	−	8143.37i	1.52132	−	1.52132i
$307$	−1783.18	−	1783.18i	−0.331503	−	0.331503i	0.521654	−	0.853157i	$-0.325315\pi$
$307$	−1783.18	−	1783.18i	−0.331503	−	0.331503i	−0.853157	+	0.521654i	$0.825315\pi$
$308$	−813.280	+	323.554i	−0.150458	+	0.0598579i
$309$		−	1912.05i		−	0.352016i
$310$	2270.76	+	2270.76i	0.416034	+	0.416034i
$311$			4313.84i			0.786544i	0.919422	+	0.393272i	$0.128657\pi$
$311$			4313.84i			0.786544i	−0.919422	+	0.393272i	$0.871343\pi$
$312$	−6238.33	+	7323.92i	−1.13197	+	1.32896i
$313$	4053.37			0.731981			0.365991	−	0.930619i	$-0.380730\pi$
$313$	4053.37			0.731981			0.365991	+	0.930619i	$0.380730\pi$
$314$	5310.91	−	5310.91i	0.954497	−	0.954497i
$315$			6397.23i			1.14426i
$316$	−2356.83			−0.419563
$317$	3620.87	+	3620.87i	0.641541	+	0.641541i	0.950934	−	0.309393i	$-0.100126\pi$
$317$	3620.87	+	3620.87i	0.641541	+	0.641541i	−0.309393	+	0.950934i	$0.600126\pi$
$318$	−244.473	+	244.473i	−0.0431111	+	0.0431111i
$319$	−723.719	+	1680.02i	−0.127023	+	0.294869i
$320$	7096.86	−	7096.86i	1.23977	−	1.23977i
$321$			692.333i			0.120381i
$322$			1916.83i			0.331742i
$323$	−3713.52	+	3713.52i	−0.639708	+	0.639708i
$324$		−	184.223i		−	0.0315883i
$325$	−10796.2	+	864.179i	−1.84267	+	0.147496i
$326$			5451.64i			0.926191i
$327$	10543.3	−	10543.3i	1.78302	−	1.78302i
$328$	−3864.73			−0.650592
$329$	4082.63			0.684141
$330$	11777.3	+	5073.43i	1.96460	+	0.846312i
$331$	−7.68480	−	7.68480i	−0.00127612	−	0.00127612i	0.706468	−	0.707745i	$-0.250287\pi$
$331$	−7.68480	−	7.68480i	−0.00127612	−	0.00127612i	−0.707745	+	0.706468i	$0.750287\pi$
$332$	−250.396	−	250.396i	−0.0413923	−	0.0413923i
$333$	8526.60	−	8526.60i	1.40317	−	1.40317i
$334$	8245.34			1.35079
$335$		−	9856.94i		−	1.60759i
$336$	1441.57	+	1441.57i	0.234059	+	0.234059i
$337$	−3784.31			−0.611704			−0.305852	−	0.952079i	$-0.598941\pi$
$337$	−3784.31			−0.611704			−0.305852	+	0.952079i	$0.598941\pi$
$338$	2871.54	−	3974.59i	0.462103	−	0.639613i
$339$	−7260.52			−1.16324
$340$	−4872.37	+	4872.37i	−0.777180	+	0.777180i
$341$	−1028.36	−	2584.86i	−0.163310	−	0.410492i
$342$			4133.58i			0.653562i
$343$	−3500.09	+	3500.09i	−0.550983	+	0.550983i
$344$	2850.68	+	2850.68i	0.446797	+	0.446797i
$345$	−12034.9	+	12034.9i	−1.87808	+	1.87808i
$346$	−6717.15	+	6717.15i	−1.04369	+	1.04369i
$347$			7923.77i			1.22585i	0.790141	+	0.612926i	$0.210007\pi$
$347$			7923.77i			1.22585i	−0.790141	+	0.612926i	$0.789993\pi$
$348$	−1263.33			−0.194602
$349$	−2110.99	−	2110.99i	−0.323778	−	0.323778i	0.526436	−	0.850215i	$-0.323528\pi$
$349$	−2110.99	−	2110.99i	−0.323778	−	0.323778i	−0.850215	+	0.526436i	$0.823528\pi$
$350$			4098.52i			0.625928i
$351$	−488.765	−	6106.18i	−0.0743258	−	0.928557i
$352$	−4343.83	+	1728.14i	−0.657747	+	0.261677i
$353$	7699.42	+	7699.42i	1.16090	+	1.16090i	0.984278	+	0.176625i	$0.0565180\pi$
$353$	7699.42	+	7699.42i	1.16090	+	1.16090i	0.176625	+	0.984278i	$0.443482\pi$
$354$		−	9222.67i		−	1.38469i
$355$		−	13215.8i		−	1.97583i
$356$	244.250	+	244.250i	0.0363630	+	0.0363630i
$357$	−5673.31	−	5673.31i	−0.841073	−	0.841073i
$358$	−5649.50	−	5649.50i	−0.834037	−	0.834037i
$359$	8643.15	+	8643.15i	1.27066	+	1.27066i	0.945740	+	0.324923i	$0.105338\pi$
$359$	8643.15	+	8643.15i	1.27066	+	1.27066i	0.324923	+	0.945740i	$0.394662\pi$
$360$			19795.9i			2.89816i
$361$			4974.02i			0.725181i
$362$	2580.33	+	2580.33i	0.374639	+	0.374639i
$363$	−7631.16	−	8072.79i	−1.10339	−	1.16725i
$364$	856.075	+	729.184i	0.123271	+	0.104999i
$365$			21969.3i			3.15048i
$366$	−7125.26	−	7125.26i	−1.01761	−	1.01761i
$367$	−2970.89			−0.422560			−0.211280	−	0.977426i	$-0.567763\pi$
$367$	−2970.89			−0.422560			−0.211280	+	0.977426i	$0.567763\pi$
$368$			3321.60i			0.470517i
$369$	4740.35	−	4740.35i	0.668760	−	0.668760i
$370$	8417.87	−	8417.87i	1.18277	−	1.18277i
$371$	104.302	+	104.302i	0.0145960	+	0.0145960i
$372$	1358.52	−	1358.52i	0.189344	−	0.189344i
$373$		−	3596.21i		−	0.499208i	−0.968348	−	0.249604i	$-0.919700\pi$
$373$		−	3596.21i		−	0.499208i	0.968348	−	0.249604i	$-0.0803005\pi$
$374$	−9151.56	+	3640.85i	−1.26528	+	0.503379i
$375$	−11812.3	+	11812.3i	−1.62663	+	1.62663i
$376$	12633.5			1.73278
$377$	2342.70	−	187.520i	0.320041	−	0.0256175i
$378$	−2318.05			−0.315417
$379$	5528.61	+	5528.61i	0.749303	+	0.749303i	0.974348	−	0.225046i	$-0.0722531\pi$
$379$	5528.61	+	5528.61i	0.749303	+	0.749303i	−0.225046	+	0.974348i	$0.572253\pi$
$380$		−	2473.22i		−	0.333877i
$381$	−6685.63			−0.898991
$382$	2076.81	−	2076.81i	0.278165	−	0.278165i
$383$	3313.92	+	3313.92i	0.442124	+	0.442124i	0.892725	−	0.450601i	$-0.148790\pi$
$383$	3313.92	+	3313.92i	0.442124	+	0.442124i	−0.450601	+	0.892725i	$0.648790\pi$
$384$	955.738	+	955.738i	0.127011	+	0.127011i
$385$	2164.54	−	5024.70i	0.286533	−	0.665149i
$386$	6524.66			0.860353
$387$	−6993.08			−0.918549
$388$	−314.373	+	314.373i	−0.0411336	+	0.0411336i
$389$		−	5132.71i		−	0.668994i	−0.942397	−	0.334497i	$-0.891434\pi$
$389$		−	5132.71i		−	0.668994i	0.942397	−	0.334497i	$-0.108566\pi$
$390$	−1314.56	−	16422.9i	−0.170680	−	2.13232i
$391$		−	13072.2i		−	1.69077i
$392$	−4866.29	+	4866.29i	−0.627002	+	0.627002i
$393$			2258.16i			0.289845i
$394$		−	3167.38i		−	0.405001i
$395$	10416.9	−	10416.9i	1.32692	−	1.32692i
$396$	1858.78	−	4314.92i	0.235877	−	0.547557i
$397$	3004.87	−	3004.87i	0.379874	−	0.379874i	−0.491182	−	0.871057i	$-0.663435\pi$
$397$	3004.87	−	3004.87i	0.379874	−	0.379874i	0.871057	+	0.491182i	$0.163435\pi$
$398$	6796.34	+	6796.34i	0.855954	+	0.855954i
$399$	2879.77			0.361326
$400$			7102.16i			0.887769i
$401$	9368.23	−	9368.23i	1.16665	−	1.16665i	0.183662	−	0.982989i	$-0.441205\pi$
$401$	9368.23	−	9368.23i	1.16665	−	1.16665i	0.982989	−	0.183662i	$-0.0587951\pi$
$402$	9730.31			1.20722
$403$	−2317.57	+	2720.87i	−0.286468	+	0.336319i
$404$			792.758i			0.0976267i
$405$	814.246	+	814.246i	0.0999018	+	0.0999018i
$406$		−	889.347i		−	0.108713i
$407$	−9582.24	+	3812.19i	−1.16701	+	0.464283i
$408$	−17555.8	−	17555.8i	−2.13025	−	2.13025i
$409$	−9310.84	+	9310.84i	−1.12565	+	1.12565i	−0.134775	+	0.990876i	$0.543031\pi$
$409$	−9310.84	+	9310.84i	−1.12565	+	1.12565i	−0.990876	+	0.134775i	$0.956969\pi$
$410$	4679.90	−	4679.90i	0.563716	−	0.563716i
$411$	6642.46	−	6642.46i	0.797198	−	0.797198i
$412$	−691.596			−0.0827002
$413$	−3934.78			−0.468809
$414$	−7275.44	−	7275.44i	−0.863691	−	0.863691i
$415$	2213.45			0.261817
$416$	4572.40	+	3894.66i	0.538895	+	0.459018i
$417$		−	7565.33i		−	0.888431i
$418$	1398.62	−	3246.71i	0.163657	−	0.379909i
$419$	−15166.7			−1.76836			−0.884180	−	0.467146i	$-0.845282\pi$
$419$	−15166.7			−1.76836			−0.884180	+	0.467146i	$0.845282\pi$
$420$	3778.44			0.438974
$421$	−9452.77	−	9452.77i	−1.09430	−	1.09430i	−0.995064	−	0.0992350i	$-0.968360\pi$
$421$	−9452.77	−	9452.77i	−1.09430	−	1.09430i	−0.0992350	−	0.995064i	$-0.531640\pi$
$422$	653.145	+	653.145i	0.0753427	+	0.0753427i
$423$	−15495.8	+	15495.8i	−1.78117	+	1.78117i
$424$	322.759	+	322.759i	0.0369683	+	0.0369683i
$425$		−	27950.6i		−	3.19013i
$426$	13046.0			1.48376
$427$	−3039.94	+	3039.94i	−0.344527	+	0.344527i
$428$	250.419			0.0282815
$429$	−4582.69	+	13516.5i	−0.515745	+	1.52117i
$430$	−6903.91			−0.774270
$431$	11216.9	−	11216.9i	1.25359	−	1.25359i	0.299493	−	0.954098i	$-0.403182\pi$
$431$	11216.9	−	11216.9i	1.25359	−	1.25359i	0.954098	−	0.299493i	$-0.0968177\pi$
$432$	−4016.86			−0.447364
$433$		−	9578.81i		−	1.06311i	−0.847023	−	0.531557i	$-0.821607\pi$
$433$		−	9578.81i		−	1.06311i	0.847023	−	0.531557i	$-0.178393\pi$
$434$	956.358	+	956.358i	0.105776	+	0.105776i
$435$	5583.80	−	5583.80i	0.615454	−	0.615454i
$436$	−3813.57	−	3813.57i	−0.418891	−	0.418891i
$437$	3317.73	+	3317.73i	0.363177	+	0.363177i
$438$	−21687.1			−2.36587
$439$	−5324.50			−0.578872			−0.289436	−	0.957197i	$-0.593468\pi$
$439$	−5324.50			−0.578872			−0.289436	+	0.957197i	$0.593468\pi$
$440$	6698.07	−	15548.7i	0.725723	−	1.68467i
$441$		−	11937.6i		−	1.28902i
$442$	9633.12	+	8205.26i	1.03665	+	0.882996i
$443$	7171.67			0.769157			0.384578	−	0.923092i	$-0.374347\pi$
$443$	7171.67			0.769157			0.384578	+	0.923092i	$0.374347\pi$
$444$	−5036.13	−	5036.13i	−0.538298	−	0.538298i
$445$	−2159.12			−0.230005
$446$	−7876.15			−0.836203
$447$	−11434.7	+	11434.7i	−1.20994	+	1.20994i
$448$	2988.93	−	2988.93i	0.315209	−	0.315209i
$449$	178.096	−	178.096i	0.0187191	−	0.0187191i	−0.697685	−	0.716404i	$-0.745787\pi$
$449$	178.096	−	178.096i	0.0187191	−	0.0187191i	0.716404	+	0.697685i	$0.245787\pi$
$450$	−15556.1	−	15556.1i	−1.62961	−	1.62961i
$451$	−5327.23	+	2119.38i	−0.556207	+	0.221281i
$452$			2626.16i			0.273283i
$453$	−3270.17	−	3270.17i	−0.339174	−	0.339174i
$454$			5971.31i			0.617285i
$455$	−7006.69	+	560.847i	−0.721931	+	0.0577866i
$456$	8911.33			0.915156
$457$	−3896.30	+	3896.30i	−0.398821	+	0.398821i	−0.877817	−	0.478996i	$-0.841001\pi$
$457$	−3896.30	+	3896.30i	−0.398821	+	0.398821i	0.478996	+	0.877817i	$0.341001\pi$
$458$			229.856i			0.0234508i
$459$	15808.4			1.60757
$460$	4353.07	+	4353.07i	0.441223	+	0.441223i
$461$	2128.38	−	2128.38i	0.215030	−	0.215030i	−0.591370	−	0.806400i	$-0.701413\pi$
$461$	2128.38	−	2128.38i	0.215030	−	0.215030i	0.806400	+	0.591370i	$0.201413\pi$
$462$	4960.15	+	2136.73i	0.499496	+	0.215173i
$463$	5461.50	−	5461.50i	0.548201	−	0.548201i	−0.377719	−	0.925920i	$-0.623291\pi$
$463$	5461.50	−	5461.50i	0.548201	−	0.548201i	0.925920	+	0.377719i	$0.123291\pi$
$464$		−	1541.11i		−	0.154191i
$465$			12009.1i			1.19765i
$466$	5037.46	−	5037.46i	0.500763	−	0.500763i
$467$		−	9422.91i		−	0.933705i	−0.884335	−	0.466853i	$-0.845388\pi$
$467$		−	9422.91i		−	0.933705i	0.884335	−	0.466853i	$-0.154612\pi$
$468$	−6016.94	+	481.622i	−0.594301	+	0.0475705i
$469$		−	4151.36i		−	0.408725i
$470$	−15298.2	+	15298.2i	−1.50139	+	1.50139i
$471$	28087.1			2.74774
$472$	−12176.0			−1.18739
$473$	5492.71	+	2366.15i	0.533944	+	0.230012i
$474$	10283.1	+	10283.1i	0.996455	+	0.996455i
$475$	7093.87	+	7093.87i	0.685240	+	0.685240i
$476$	−2052.05	+	2052.05i	−0.197596	+	0.197596i
$477$	−791.770			−0.0760014
$478$			334.343i			0.0319927i
$479$	−3849.28	−	3849.28i	−0.367177	−	0.367177i	0.499269	−	0.866447i	$-0.333602\pi$
$479$	−3849.28	−	3849.28i	−0.367177	−	0.367177i	−0.866447	+	0.499269i	$0.833602\pi$
$480$	20181.1			1.91904
$481$	10086.5	+	8591.41i	0.956140	+	0.814417i
$482$	−9018.19			−0.852215
$483$	−5068.64	+	5068.64i	−0.477497	+	0.477497i
$484$	−2919.96	+	2760.22i	−0.274226	+	0.259224i
$485$		−	2778.99i		−	0.260181i
$486$	−6372.50	+	6372.50i	−0.594779	+	0.594779i
$487$	8101.91	+	8101.91i	0.753866	+	0.753866i	0.975198	−	0.221333i	$-0.0710407\pi$
$487$	8101.91	+	8101.91i	0.753866	+	0.753866i	−0.221333	+	0.975198i	$0.571041\pi$
$488$	−9406.96	+	9406.96i	−0.872609	+	0.872609i
$489$	−14415.7	+	14415.7i	−1.33313	+	1.33313i
$490$		−	11785.4i		−	1.08655i
$491$	−327.105			−0.0300653			−0.0150326	−	0.999887i	$-0.504785\pi$
$491$	−327.105			−0.0300653			−0.0150326	+	0.999887i	$0.504785\pi$
$492$	−2799.83	−	2799.83i	−0.256557	−	0.256557i
$493$			6065.08i			0.554072i
$494$	−4527.38	+	362.392i	−0.412341	+	0.0330056i
$495$	10855.9	+	27287.1i	0.985729	+	2.47771i
$496$	1657.23	+	1657.23i	0.150024	+	0.150024i
$497$		−	5565.97i		−	0.502350i
$498$			2185.02i			0.196612i
$499$	−9047.61	−	9047.61i	−0.811677	−	0.811677i	0.173208	−	0.984885i	$-0.444587\pi$
$499$	−9047.61	−	9047.61i	−0.811677	−	0.811677i	−0.984885	+	0.173208i	$0.944587\pi$
$500$	4272.56	+	4272.56i	0.382149	+	0.382149i
$501$	21803.0	+	21803.0i	1.94428	+	1.94428i
$502$	−1487.77	−	1487.77i	−0.132276	−	0.132276i
$503$		−	489.945i		−	0.0434305i	−0.999764	−	0.0217153i	$-0.993087\pi$
$503$		−	489.945i		−	0.0434305i	0.999764	−	0.0217153i	$-0.00691273\pi$
$504$			8337.29i			0.736850i
$505$	−3503.91	−	3503.91i	−0.308757	−	0.308757i
$506$	3252.80	+	8176.17i	0.285780	+	0.718331i
$507$	18103.1	−	2916.79i	1.58577	−	0.255501i
$508$			2418.22i			0.211203i
$509$	−1275.85	−	1275.85i	−0.111103	−	0.111103i	0.649370	−	0.760473i	$-0.275033\pi$
$509$	−1275.85	−	1275.85i	−0.111103	−	0.111103i	−0.760473	+	0.649370i	$0.775033\pi$
$510$	42517.5			3.69158
$511$			9252.63i			0.801003i
$512$	7060.81	−	7060.81i	0.609466	−	0.609466i
$513$	−4012.18	+	4012.18i	−0.345306	+	0.345306i
$514$	−345.417	−	345.417i	−0.0296414	−	0.0296414i
$515$	3056.79	−	3056.79i	0.261550	−	0.261550i
$516$			4130.38i			0.352383i
$517$	17414.3	−	6928.08i	1.48139	−	0.589356i
$518$	3545.28	−	3545.28i	0.300716	−	0.300716i
$519$	−35524.0			−3.00449
$520$	−21681.9	+	1735.52i	−1.82849	+	0.146360i
$521$	7553.47			0.635170			0.317585	−	0.948230i	$-0.397128\pi$
$521$	7553.47			0.635170			0.317585	+	0.948230i	$0.397128\pi$
$522$	3375.56	+	3375.56i	0.283035	+	0.283035i
$523$		−	6618.66i		−	0.553372i	−0.960960	−	0.276686i	$-0.910764\pi$
$523$		−	6618.66i		−	0.553372i	0.960960	−	0.276686i	$-0.0892362\pi$
$524$	816.786			0.0680944
$525$	−10837.6	+	10837.6i	−0.900938	+	0.900938i
$526$	−8333.31	−	8333.31i	−0.690778	−	0.690778i
$527$	−6522.07	−	6522.07i	−0.539100	−	0.539100i
$528$	8595.24	+	3702.66i	0.708447	+	0.305185i
$529$	488.051			0.0401127
$530$	−781.674			−0.0640637
$531$	14934.7	−	14934.7i	1.22055	−	1.22055i
$532$		−	1041.62i		−	0.0848874i
$533$	5607.55	+	4776.37i	0.455703	+	0.388157i
$534$		−	2131.38i		−	0.172723i
$535$	−1106.83	+	1106.83i	−0.0894438	+	0.0894438i
$536$		−	12846.2i		−	1.03521i
$537$		−	29877.7i		−	2.40096i
$538$	−6069.04	+	6069.04i	−0.486347	+	0.486347i
$539$	−4039.17	+	9376.42i	−0.322782	+	0.749297i
$540$	−5264.23	+	5264.23i	−0.419512	+	0.419512i
$541$	4687.67	+	4687.67i	0.372530	+	0.372530i	0.868398	−	0.495868i	$-0.165150\pi$
$541$	4687.67	+	4687.67i	0.372530	+	0.372530i	−0.495868	+	0.868398i	$0.665150\pi$
$542$	−13002.5			−1.03045
$543$			13646.2i			1.07848i
$544$	−10960.3	+	10960.3i	−0.863820	+	0.863820i
$545$	33711.2			2.64959
$546$	−553.642	−	6916.68i	−0.0433950	−	0.542137i
$547$			11229.3i			0.877748i	0.898549	+	0.438874i	$0.144623\pi$
$547$			11229.3i			0.877748i	−0.898549	+	0.438874i	$0.855377\pi$
$548$	−2402.60	−	2402.60i	−0.187288	−	0.187288i
$549$		−	23076.5i		−	1.79396i
$550$	6955.05	+	17482.1i	0.539208	+	1.35534i
$551$	−1539.32	−	1539.32i	−0.119015	−	0.119015i
$552$	−15684.7	+	15684.7i	−1.20939	+	1.20939i
$553$	4387.22	−	4387.22i	0.337366	−	0.337366i
$554$	−9988.36	+	9988.36i	−0.766001	+	0.766001i
$555$	44518.4			3.40487
$556$	−2736.41			−0.208722
$557$	−14580.0	−	14580.0i	−1.10911	−	1.10911i	−0.993268	−	0.115840i	$-0.963044\pi$
$557$	−14580.0	−	14580.0i	−1.10911	−	1.10911i	−0.115840	−	0.993268i	$-0.536956\pi$
$558$	−7259.82			−0.550775
$559$	−613.086	−	7659.32i	−0.0463878	−	0.579525i
$560$			4609.25i			0.347815i
$561$	−33826.7	−	14571.9i	−2.54575	−	1.09666i
$562$	−7481.73			−0.561562
$563$	15074.7			1.12846			0.564228	−	0.825619i	$-0.309174\pi$
$563$	15074.7			1.12846			0.564228	+	0.825619i	$0.309174\pi$
$564$	9152.41	+	9152.41i	0.683309	+	0.683309i
$565$	−11607.4	−	11607.4i	−0.864293	−	0.864293i
$566$	368.675	−	368.675i	0.0273791	−	0.0273791i
$567$	342.929	+	342.929i	0.0253998	+	0.0253998i
$568$		−	17223.6i		−	1.27234i
$569$	−12928.2			−0.952512			−0.476256	−	0.879307i	$-0.658006\pi$
$569$	−12928.2			−0.952512			−0.476256	+	0.879307i	$0.658006\pi$
$570$	−10790.9	+	10790.9i	−0.792952	+	0.792952i
$571$	2005.86			0.147010			0.0735048	−	0.997295i	$-0.476582\pi$
$571$	2005.86			0.147010			0.0735048	+	0.997295i	$0.476582\pi$
$572$	4888.96	+	1657.58i	0.357373	+	0.121166i
$573$	10983.4			0.800761
$574$	1970.99	−	1970.99i	0.143323	−	0.143323i
$575$	−24971.6			−1.81111
$576$			22689.3i			1.64129i
$577$	−11045.2	−	11045.2i	−0.796911	−	0.796911i	0.185696	−	0.982607i	$-0.440546\pi$
$577$	−11045.2	−	11045.2i	−0.796911	−	0.796911i	−0.982607	+	0.185696i	$0.940546\pi$
$578$	−15337.6	+	15337.6i	−1.10374	+	1.10374i
$579$	17253.0	+	17253.0i	1.23836	+	1.23836i
$580$	−2019.68	−	2019.68i	−0.144591	−	0.144591i
$581$	932.220			0.0665663
$582$	2743.29			0.195383
$583$	621.896	+	267.900i	0.0441789	+	0.0190314i
$584$			28631.9i			2.02876i
$585$	24465.6	−	28723.0i	1.72910	−	2.03000i
$586$	3997.34			0.281789
$587$	−7105.37	−	7105.37i	−0.499608	−	0.499608i	0.411708	−	0.911316i	$-0.364932\pi$
$587$	−7105.37	−	7105.37i	−0.499608	−	0.499608i	−0.911316	+	0.411708i	$0.864932\pi$
$588$	−7050.82			−0.494508
$589$	3310.60			0.231598
$590$	14744.2	−	14744.2i	1.02883	−	1.02883i
$591$	8375.44	−	8375.44i	0.582943	−	0.582943i
$592$	6143.48	−	6143.48i	0.426513	−	0.426513i
$593$	19035.5	+	19035.5i	1.31821	+	1.31821i	0.915196	+	0.403009i	$0.132036\pi$
$593$	19035.5	+	19035.5i	1.31821	+	1.31821i	0.403009	+	0.915196i	$0.367964\pi$
$594$	−9887.57	+	3933.66i	−0.682983	+	0.271717i
$595$		−	18139.8i		−	1.24985i
$596$	4135.99	+	4135.99i	0.284256	+	0.284256i
$597$			35942.8i			2.46406i
$598$	7330.73	−	8606.41i	0.501297	−	0.588532i
$599$	−19400.6			−1.32335			−0.661675	−	0.749791i	$-0.730154\pi$
$599$	−19400.6			−1.32335			−0.661675	+	0.749791i	$0.730154\pi$
$600$	−33536.5	+	33536.5i	−2.28187	+	2.28187i
$601$			7774.81i			0.527689i	0.964565	+	0.263845i	$0.0849906\pi$
$601$			7774.81i			0.527689i	−0.964565	+	0.263845i	$0.915009\pi$
$602$	−2907.66			−0.196856
$603$	15756.7	+	15756.7i	1.06412	+	1.06412i
$604$	−1182.83	+	1182.83i	−0.0796833	+	0.0796833i
$605$	706.019	−	25105.8i	0.0474442	−	1.68710i
$606$	3458.90	−	3458.90i	0.231862	−	0.231862i
$607$			7903.47i			0.528488i	0.964456	+	0.264244i	$0.0851223\pi$
$607$			7903.47i			0.528488i	−0.964456	+	0.264244i	$0.914878\pi$
$608$		−	5563.44i		−	0.371097i
$609$	2351.68	−	2351.68i	0.156478	−	0.156478i
$610$		−	22782.2i		−	1.51217i
$611$	−18330.6	−	15613.6i	−1.21371	−	1.03381i
$612$		−	15577.4i		−	1.02889i
$613$	14873.0	−	14873.0i	0.979957	−	0.979957i	−0.0198464	−	0.999803i	$-0.506318\pi$
$613$	14873.0	−	14873.0i	0.979957	−	0.979957i	0.999803	+	0.0198464i	$0.00631773\pi$
$614$	5628.27			0.369932
$615$	24749.9			1.62279
$616$	2820.97	−	6548.52i	0.184513	−	0.428324i
$617$	5673.77	+	5673.77i	0.370207	+	0.370207i	0.867552	−	0.497346i	$-0.165692\pi$
$617$	5673.77	+	5673.77i	0.370207	+	0.370207i	−0.497346	+	0.867552i	$0.665692\pi$
$618$	3017.52	+	3017.52i	0.196412	+	0.196412i
$619$	2002.18	−	2002.18i	0.130007	−	0.130007i	−0.639109	−	0.769116i	$-0.720697\pi$
$619$	2002.18	−	2002.18i	0.130007	−	0.130007i	0.769116	+	0.639109i	$0.220697\pi$
$620$	4343.72			0.281368
$621$		−	14123.5i		−	0.912653i
$622$	−6807.91	−	6807.91i	−0.438862	−	0.438862i
$623$	−909.339			−0.0584782
$624$	−959.383	−	11985.6i	−0.0615482	−	0.768926i
$625$	−8884.79			−0.568627
$626$	−6396.86	+	6396.86i	−0.408418	+	0.408418i
$627$	12283.6	−	4886.88i	0.782389	−	0.311265i
$628$		−	10159.2i		−	0.645535i
$629$	−24177.8	+	24177.8i	−1.53264	+	1.53264i
$630$	−10095.8	−	10095.8i	−0.638456	−	0.638456i
$631$	4767.59	−	4767.59i	0.300784	−	0.300784i	−0.540537	−	0.841321i	$-0.681779\pi$
$631$	4767.59	−	4767.59i	0.300784	−	0.300784i	0.841321	+	0.540537i	$0.181779\pi$
$632$	13576.1	−	13576.1i	0.854472	−	0.854472i
$633$			3454.20i			0.216891i
$634$	−11428.6			−0.715912
$635$	−10688.3	−	10688.3i	−0.667956	−	0.667956i
$636$			467.649i			0.0291564i
$637$	13074.9	−	1046.58i	0.813263	−	0.0650971i
$638$	−1509.19	−	3793.48i	−0.0936513	−	0.235400i
$639$	21125.9	+	21125.9i	1.30787	+	1.30787i
$640$			3055.87i			0.188740i
$641$			6522.34i			0.401899i	0.979602	+	0.200949i	$0.0644027\pi$
$641$			6522.34i			0.401899i	−0.979602	+	0.200949i	$0.935597\pi$
$642$	−1092.61	−	1092.61i	−0.0671681	−	0.0671681i
$643$	−7423.77	−	7423.77i	−0.455311	−	0.455311i	0.441802	−	0.897113i	$-0.354339\pi$
$643$	−7423.77	−	7423.77i	−0.455311	−	0.455311i	−0.897113	+	0.441802i	$0.854339\pi$
$644$	1833.34	+	1833.34i	0.112180	+	0.112180i
$645$	−18255.9	−	18255.9i	−1.11446	−	1.11446i
$646$		−	11721.0i		−	0.713867i
$647$			12379.9i			0.752246i	0.926570	+	0.376123i	$0.122743\pi$
$647$			12379.9i			0.752246i	−0.926570	+	0.376123i	$0.877257\pi$
$648$	1061.18	+	1061.18i	0.0643319	+	0.0643319i
$649$	−16783.7	+	6677.20i	−1.01513	+	0.403856i
$650$	15674.4	−	18402.0i	0.945845	−	1.11044i
$651$			5057.75i			0.304499i
$652$	5214.19	+	5214.19i	0.313196	+	0.313196i
$653$	22023.3			1.31981			0.659906	−	0.751348i	$-0.270596\pi$
$653$	22023.3			1.31981			0.659906	+	0.751348i	$0.270596\pi$
$654$			33278.1i			1.98972i
$655$	−3610.11	+	3610.11i	−0.215357	+	0.215357i
$656$	3415.46	−	3415.46i	0.203279	−	0.203279i
$657$	−35118.9	−	35118.9i	−2.08541	−	2.08541i
$658$	−6443.03	+	6443.03i	−0.381725	+	0.381725i
$659$			2617.72i			0.154737i	0.997003	+	0.0773685i	$0.0246518\pi$
$659$			2617.72i			0.154737i	−0.997003	+	0.0773685i	$0.975348\pi$
$660$	16116.8	−	6411.89i	0.950524	−	0.378155i
$661$	−14389.5	+	14389.5i	−0.846729	+	0.846729i	−0.989723	−	0.142994i	$-0.954327\pi$
$661$	−14389.5	+	14389.5i	−0.846729	+	0.846729i	0.142994	+	0.989723i	$0.454327\pi$
$662$	24.2556			0.00142405
$663$	3775.67	+	47169.6i	0.221169	+	2.76307i
$664$	2884.71			0.168597
$665$	4603.88	+	4603.88i	0.268467	+	0.268467i
$666$			26912.6i			1.56583i
$667$	5418.65			0.314559
$668$	7886.22	−	7886.22i	0.456777	−	0.456777i
$669$	−20826.7	−	20826.7i	−1.20360	−	1.20360i
$670$	15555.8	+	15555.8i	0.896974	+	0.896974i
$671$	−7808.08	+	18125.4i	−0.449221	+	1.04281i
$672$	8499.51			0.487910
$673$	26911.5			1.54140			0.770701	−	0.637197i	$-0.219906\pi$
$673$	26911.5			1.54140			0.770701	+	0.637197i	$0.219906\pi$
$674$	5972.23	−	5972.23i	0.341308	−	0.341308i
$675$		−	30198.5i		−	1.72199i
$676$	−1055.01	−	6547.95i	−0.0600258	−	0.372550i
$677$			16951.7i			0.962346i	0.876626	+	0.481173i	$0.159789\pi$
$677$			16951.7i			0.962346i	−0.876626	+	0.481173i	$0.840211\pi$
$678$	11458.2	−	11458.2i	0.649043	−	0.649043i
$679$		−	1170.41i		−	0.0661503i
$680$		−	56132.7i		−	3.16558i
$681$	−15789.8	+	15789.8i	−0.888497	+	0.888497i
$682$	5702.22	+	2456.40i	0.320160	+	0.137919i
$683$	−9415.45	+	9415.45i	−0.527485	+	0.527485i	−0.919822	−	0.392337i	$-0.871667\pi$
$683$	−9415.45	+	9415.45i	−0.527485	+	0.527485i	0.392337	+	0.919822i	$0.371667\pi$
$684$	3953.54	+	3953.54i	0.221005	+	0.221005i
$685$	21238.5			1.18465
$686$		−	11047.4i		−	0.614856i
$687$	−607.804	+	607.804i	−0.0337542	+	0.0337542i
$688$	−5038.57			−0.279206
$689$	−69.4147	−	867.203i	−0.00383816	−	0.0479503i
$690$		−	37985.9i		−	2.09580i
$691$	14225.6	+	14225.6i	0.783168	+	0.783168i	0.980364	−	0.197196i	$-0.0631836\pi$
$691$	14225.6	+	14225.6i	0.783168	+	0.783168i	−0.197196	+	0.980364i	$0.563184\pi$
$692$			12849.2i			0.705855i
$693$	4572.08	+	11492.3i	0.250619	+	0.629951i
$694$	−12505.0	−	12505.0i	−0.683979	−	0.683979i
$695$	12094.7	−	12094.7i	0.660110	−	0.660110i
$696$	7277.18	−	7277.18i	0.396323	−	0.396323i
$697$	−13441.6	+	13441.6i	−0.730468	+	0.730468i
$698$	6662.94			0.361313
$699$	26640.9			1.44156
$700$	3920.01	+	3920.01i	0.211660	+	0.211660i
$701$	−2621.24			−0.141231			−0.0706155	−	0.997504i	$-0.522496\pi$
$701$	−2621.24			−0.141231			−0.0706155	+	0.997504i	$0.522496\pi$
$702$	10407.9	+	8865.16i	0.559571	+	0.476629i
$703$		−	12272.6i		−	0.658423i
$704$	7677.04	−	17821.3i	0.410994	−	0.954068i
$705$	−80905.6			−4.32210
$706$	−24301.8			−1.29548
$707$	−1475.71	−	1475.71i	−0.0785006	−	0.0785006i
$708$	−8820.97	−	8820.97i	−0.468238	−	0.468238i
$709$	−17312.4	+	17312.4i	−0.917042	+	0.917042i	−0.996813	−	0.0797714i	$-0.974581\pi$
$709$	−17312.4	+	17312.4i	−0.917042	+	0.917042i	0.0797714	+	0.996813i	$0.474581\pi$
$710$	20856.5	+	20856.5i	1.10244	+	1.10244i
$711$			33303.8i			1.75667i
$712$	−2813.91			−0.148112
$713$	−5826.94	+	5826.94i	−0.306060	+	0.306060i
$714$	17906.7			0.938575
$715$	−28935.1	+	14282.4i	−1.51344	+	0.747037i
$716$	−10806.9			−0.564067
$717$	−884.097	+	884.097i	−0.0460491	+	0.0460491i
$718$	−27280.5			−1.41797
$719$			18115.8i			0.939646i	0.882761	+	0.469823i	$0.155682\pi$
$719$			18115.8i			0.939646i	−0.882761	+	0.469823i	$0.844318\pi$
$720$	−17494.7	−	17494.7i	−0.905538	−	0.905538i
$721$	1287.40	−	1287.40i	0.0664984	−	0.0664984i
$722$	−7849.78	−	7849.78i	−0.404624	−	0.404624i
$723$	−23846.6	−	23846.6i	−1.22665	−	1.22665i
$724$	4935.89			0.253372
$725$	11586.0			0.593508
$726$	24783.3	+	696.949i	1.26693	+	0.0356284i
$727$		−	14200.2i		−	0.724426i	−0.932095	−	0.362213i	$-0.882021\pi$
$727$		−	14200.2i		−	0.724426i	0.932095	−	0.362213i	$-0.117979\pi$
$728$	−9131.58	+	730.932i	−0.464889	+	0.0372117i
$729$	−32053.7			−1.62850
$730$	−34671.0	−	34671.0i	−1.75785	−	1.75785i
$731$	19829.4			1.00330
$732$	−13629.8			−0.688215
$733$	−3163.26	+	3163.26i	−0.159396	+	0.159396i	−0.782299	−	0.622903i	$-0.785953\pi$
$733$	−3163.26	+	3163.26i	−0.159396	+	0.159396i	0.622903	+	0.782299i	$0.285953\pi$
$734$	4688.54	−	4688.54i	0.235773	−	0.235773i
$735$	31163.9	−	31163.9i	1.56394	−	1.56394i
$736$	9792.11	+	9792.11i	0.490410	+	0.490410i
$737$	−7044.73	−	17707.5i	−0.352098	−	0.885026i
$738$			14962.0i			0.746287i
$739$	−8338.82	−	8338.82i	−0.415086	−	0.415086i	0.468420	−	0.883506i	$-0.344823\pi$
$739$	−8338.82	−	8338.82i	−0.415086	−	0.415086i	−0.883506	+	0.468420i	$0.844823\pi$
$740$		−	16102.5i		−	0.799917i
$741$	−12929.9	−	11013.4i	−0.641016	−	0.546002i
$742$	−329.211			−0.0162880
$743$	−6605.65	+	6605.65i	−0.326161	+	0.326161i	−0.851125	−	0.524963i	$-0.824079\pi$
$743$	−6605.65	+	6605.65i	−0.326161	+	0.326161i	0.524963	+	0.851125i	$0.324079\pi$
$744$			15651.0i			0.771228i
$745$	−36561.3			−1.79799
$746$	5675.38	+	5675.38i	0.278540	+	0.278540i
$747$	−3538.29	+	3538.29i	−0.173306	+	0.173306i
$748$	−5270.70	+	12235.2i	−0.257641	+	0.598081i
$749$	−466.154	+	466.154i	−0.0227409	+	0.0227409i
$750$		−	37283.4i		−	1.81520i
$751$		−	36643.4i		−	1.78048i	−0.455496	−	0.890238i	$-0.650538\pi$
$751$		−	36643.4i		−	1.78048i	0.455496	−	0.890238i	$-0.349462\pi$
$752$	−11164.9	+	11164.9i	−0.541411	+	0.541411i
$753$		−	7868.16i		−	0.380786i
$754$	−3401.22	+	3993.09i	−0.164277	+	0.192864i
$755$		−	10456.0i		−	0.504017i
$756$	−2217.09	+	2217.09i	−0.106660	+	0.106660i
$757$	−4977.33			−0.238975			−0.119487	−	0.992836i	$-0.538125\pi$
$757$	−4977.33			−0.238975			−0.119487	+	0.992836i	$0.538125\pi$
$758$	−17450.0			−0.836166
$759$	−13018.8	+	30221.4i	−0.622598	+	1.44528i
$760$	14246.5	+	14246.5i	0.679966	+	0.679966i
$761$	−22726.0	−	22726.0i	−1.08255	−	1.08255i	−0.996271	−	0.0862760i	$-0.972503\pi$
$761$	−22726.0	−	22726.0i	−1.08255	−	1.08255i	−0.0862760	−	0.996271i	$-0.527497\pi$
$762$	10551.0	−	10551.0i	0.501603	−	0.501603i
$763$	14197.9			0.673653
$764$		−	3972.72i		−	0.188126i
$765$	68850.5	+	68850.5i	3.25398	+	3.25398i
$766$	−10459.8			−0.493378
$767$	17666.8	+	15048.2i	0.831698	+	0.708420i
$768$	32496.7			1.52685
$769$	11321.3	−	11321.3i	0.530891	−	0.530891i	−0.389947	−	0.920837i	$-0.627507\pi$
$769$	11321.3	−	11321.3i	0.530891	−	0.530891i	0.920837	+	0.389947i	$0.127507\pi$
$770$	4513.78	+	11345.7i	0.211254	+	0.531003i
$771$		−	1826.76i		−	0.0853295i
$772$	6240.48	−	6240.48i	0.290932	−	0.290932i
$773$	−5899.71	−	5899.71i	−0.274512	−	0.274512i	0.556401	−	0.830914i	$-0.312182\pi$
$773$	−5899.71	−	5899.71i	−0.274512	−	0.274512i	−0.830914	+	0.556401i	$0.812182\pi$
$774$	11036.2	−	11036.2i	0.512516	−	0.512516i
$775$	−12459.0	+	12459.0i	−0.577472	+	0.577472i
$776$		−	3621.77i		−	0.167544i
$777$	18749.4			0.865679
$778$	8100.22	+	8100.22i	0.373274	+	0.373274i
$779$		−	6822.95i		−	0.313809i
$780$	−16964.9	−	14450.3i	−0.778769	−	0.663337i
$781$	−9445.27	−	23741.4i	−0.432751	−	1.08775i
$782$	20630.0	+	20630.0i	0.943385	+	0.943385i
$783$			6552.85i			0.299080i
$784$		−	8601.16i		−	0.391817i
$785$	44902.6	+	44902.6i	2.04158	+	2.04158i
$786$	−3563.74	−	3563.74i	−0.161723	−	0.161723i
$787$	−8149.20	−	8149.20i	−0.369107	−	0.369107i	0.498044	−	0.867152i	$-0.334052\pi$
$787$	−8149.20	−	8149.20i	−0.369107	−	0.369107i	−0.867152	+	0.498044i	$0.834052\pi$
$788$	−3029.43	−	3029.43i	−0.136953	−	0.136953i
$789$		−	44071.2i		−	1.98856i
$790$			32879.2i			1.48074i
$791$	−4888.57	−	4888.57i	−0.219744	−	0.219744i
$792$	14148.1	+	35562.4i	0.634761	+	1.59552i
$793$	25275.0	−	2023.12i	1.13183	−	0.0905968i
$794$			9484.31i			0.423911i
$795$	−2066.96	−	2066.96i	−0.0922109	−	0.0922109i
$796$	13000.6			0.578889
$797$		−	5626.08i		−	0.250045i	−0.992154	−	0.125023i	$-0.960100\pi$
$797$		−	5626.08i		−	0.250045i	0.992154	−	0.125023i	$-0.0399003\pi$
$798$	−4544.73	+	4544.73i	−0.201606	+	0.201606i
$799$	43939.5	−	43939.5i	1.94552	−	1.94552i
$800$	20937.2	+	20937.2i	0.925303	+	0.925303i
$801$	3451.45	−	3451.45i	0.152248	−	0.152248i
$802$			29569.1i			1.30190i
$803$	15701.4	+	39466.8i	0.690026	+	1.73444i
$804$	9306.51	−	9306.51i	0.408228	−	0.408228i
$805$	−16206.4			−0.709566
$806$	−636.470	−	7951.46i	−0.0278148	−	0.347492i
$807$	−32096.5			−1.40006
$808$	−4566.53	−	4566.53i	−0.198824	−	0.198824i
$809$			34849.6i			1.51452i	0.653114	+	0.757260i	$0.273462\pi$
$809$			34849.6i			1.51452i	−0.653114	+	0.757260i	$0.726538\pi$
$810$	−2570.02			−0.111483
$811$	13835.0	−	13835.0i	0.599029	−	0.599029i	−0.341025	−	0.940054i	$-0.610774\pi$
$811$	13835.0	−	13835.0i	0.599029	−	0.599029i	0.940054	+	0.341025i	$0.110774\pi$
$812$	−850.612	−	850.612i	−0.0367618	−	0.0367618i
$813$	−34382.2	−	34382.2i	−1.48319	−	1.48319i
$814$	9106.05	−	21138.5i	0.392097	−	0.910202i
$815$	−46092.5			−1.98104
$816$	31029.9			1.33120
$817$	−5032.70	+	5032.70i	−0.215510	+	0.215510i
$818$		−	29387.9i		−	1.25614i
$819$	10303.9	−	12097.0i	0.439620	−	0.516122i
$820$		−	8952.13i		−	0.381246i
$821$	1760.70	−	1760.70i	0.0748464	−	0.0748464i	−0.668693	−	0.743539i	$-0.733146\pi$
$821$	1760.70	−	1760.70i	0.0748464	−	0.0748464i	0.743539	+	0.668693i	$0.233146\pi$
$822$			20965.7i			0.889614i
$823$		−	10464.3i		−	0.443210i	−0.975136	−	0.221605i	$-0.928870\pi$
$823$		−	10464.3i		−	0.443210i	0.975136	−	0.221605i	$-0.0711296\pi$
$824$	3983.81	−	3983.81i	0.168425	−	0.168425i
$825$	−27836.4	+	64618.6i	−1.17471	+	2.72694i
$826$	6209.70	−	6209.70i	0.261578	−	0.261578i
$827$	−15359.6	−	15359.6i	−0.645834	−	0.645834i	0.306150	−	0.951983i	$-0.400959\pi$
$827$	−15359.6	−	15359.6i	−0.645834	−	0.645834i	−0.951983	+	0.306150i	$0.900959\pi$
$828$	−13917.1			−0.584122
$829$		−	12487.0i		−	0.523152i	−0.965183	−	0.261576i	$-0.915758\pi$
$829$		−	12487.0i		−	0.523152i	0.965183	−	0.261576i	$-0.0842421\pi$
$830$	−3493.17	+	3493.17i	−0.146084	+	0.146084i
$831$	−52824.0			−2.20511
$832$	−24850.9	+	1989.17i	−1.03552	+	0.0828872i
$833$			33850.0i			1.40796i
$834$	11939.3	+	11939.3i	0.495711	+	0.495711i
$835$			69712.6i			2.88923i
$836$	−1767.60	−	4443.01i	−0.0731265	−	0.183809i
$837$	−7046.60	−	7046.60i	−0.290999	−	0.290999i
$838$	23935.5	−	23935.5i	0.986679	−	0.986679i
$839$	7183.61	−	7183.61i	0.295597	−	0.295597i	−0.543690	−	0.839286i	$-0.682973\pi$
$839$	7183.61	−	7183.61i	0.295597	−	0.295597i	0.839286	+	0.543690i	$0.182973\pi$
$840$	−21765.0	+	21765.0i	−0.894004	+	0.894004i
$841$	21874.9			0.896918
$842$	29835.9			1.22116
$843$	−19783.8	−	19783.8i	−0.808291	−	0.808291i
$844$	1249.40			0.0509549
$845$	33604.3	+	24278.2i	1.36808	+	0.988398i
$846$		−	48909.7i		−	1.98765i
$847$	297.348	−	10573.6i	0.0120626	−	0.428941i
$848$	−570.477			−0.0231017
$849$	1949.76			0.0788170
$850$	44110.5	+	44110.5i	1.77997	+	1.77997i
$851$	21600.9	+	21600.9i	0.870115	+	0.870115i
$852$	12477.8	−	12477.8i	0.501738	−	0.501738i
$853$	25358.1	+	25358.1i	1.01787	+	1.01787i	0.999837	+	0.0180328i	$0.00574034\pi$
$853$	25358.1	+	25358.1i	1.01787	+	1.01787i	0.0180328	+	0.999837i	$0.494260\pi$
$854$		−	9595.01i		−	0.384467i
$855$	−34948.5			−1.39791
$856$	−1442.49	+	1442.49i	−0.0575974	+	0.0575974i
$857$	−839.524			−0.0334628			−0.0167314	−	0.999860i	$-0.505326\pi$
$857$	−839.524			−0.0334628			−0.0167314	+	0.999860i	$0.505326\pi$
$858$	−14098.9	−	28563.3i	−0.560990	−	1.13652i
$859$	9248.61			0.367356			0.183678	−	0.982986i	$-0.441200\pi$
$859$	9248.61			0.367356			0.183678	+	0.982986i	$0.441200\pi$
$860$	−6603.21	+	6603.21i	−0.261823	+	0.261823i
$861$	10423.7			0.412589
$862$			35404.0i			1.39892i
$863$	−6734.81	−	6734.81i	−0.265650	−	0.265650i	0.561695	−	0.827344i	$-0.310150\pi$
$863$	−6734.81	−	6734.81i	−0.265650	−	0.265650i	−0.827344	+	0.561695i	$0.810150\pi$
$864$	−11841.7	+	11841.7i	−0.466278	+	0.466278i
$865$	−56792.1	−	56792.1i	−2.23236	−	2.23236i
$866$	15116.9	+	15116.9i	0.593178	+	0.593178i
$867$	−81113.7			−3.17735
$868$	1829.41			0.0715370
$869$	11268.6	−	26158.5i	0.439884	−	1.02113i
$870$			17624.2i			0.686801i
$871$	−15876.5	+	18639.3i	−0.617628	+	0.725106i
$872$	43934.6			1.70621
$873$	4442.34	+	4442.34i	0.172223	+	0.172223i
$874$	−10471.8			−0.405279
$875$	−15906.7			−0.614565
$876$	−20742.5	+	20742.5i	−0.800028	+	0.800028i
$877$	−2738.25	+	2738.25i	−0.105432	+	0.105432i	−0.757855	−	0.652423i	$-0.773753\pi$
$877$	−2738.25	+	2738.25i	−0.105432	+	0.105432i	0.652423	+	0.757855i	$0.273753\pi$
$878$	8402.90	−	8402.90i	0.322989	−	0.322989i
$879$	10570.1	+	10570.1i	0.405597	+	0.405597i
$880$	7821.75	+	19660.6i	0.299626	+	0.753135i
$881$			17078.3i			0.653103i	0.945179	+	0.326552i	$0.105887\pi$
$881$			17078.3i			0.653103i	−0.945179	+	0.326552i	$0.894113\pi$
$882$	18839.5	+	18839.5i	0.719227	+	0.719227i
$883$			34257.6i			1.30562i	0.757524	+	0.652808i	$0.226409\pi$
$883$			34257.6i			1.30562i	−0.757524	+	0.652808i	$0.773591\pi$
$884$	17061.4	−	1365.67i	0.649138	−	0.0519599i
$885$	77975.7			2.96172
$886$	−11318.0	+	11318.0i	−0.429161	+	0.429161i
$887$		−	34533.4i		−	1.30724i	−0.756825	−	0.653618i	$-0.773250\pi$
$887$		−	34533.4i		−	1.30724i	0.756825	−	0.653618i	$-0.226750\pi$
$888$	58019.3			2.19257
$889$	−4501.50	−	4501.50i	−0.169826	−	0.169826i
$890$	3407.43	−	3407.43i	0.128334	−	0.128334i
$891$	2044.69	+	880.813i	0.0768797	+	0.0331182i
$892$	−7533.11	+	7533.11i	−0.282766	+	0.282766i
$893$			22303.7i			0.835794i
$894$		−	36091.6i		−	1.35021i
$895$	47765.3	−	47765.3i	1.78393	−	1.78393i
$896$			1287.01i			0.0479867i
$897$	42142.2	−	3373.25i	1.56866	−	0.125562i
$898$			562.128i			0.0208891i
$899$	2703.51	−	2703.51i	0.100297	−	0.100297i
$900$	−29757.2			−1.10212
$901$	2245.12			0.0830142
$902$	5062.49	−	11751.9i	0.186876	−	0.433809i
$903$	−7688.67	−	7688.67i	−0.283348	−	0.283348i
$904$	−15127.5	−	15127.5i	−0.556562	−	0.556562i
$905$	−21816.2	+	21816.2i	−0.801320	+	0.801320i
$906$	10321.7			0.378493
$907$			26779.7i			0.980381i	0.871615	+	0.490191i	$0.163073\pi$
$907$			26779.7i			0.980381i	−0.871615	+	0.490191i	$0.836927\pi$
$908$	5711.23	+	5711.23i	0.208738	+	0.208738i
$909$	11202.3			0.408753
$910$	10172.6	−	11942.8i	0.370568	−	0.435054i
$911$	−37643.0			−1.36901			−0.684506	−	0.729008i	$-0.739982\pi$
$911$	−37643.0			−1.36901			−0.684506	+	0.729008i	$0.739982\pi$
$912$	−7875.38	+	7875.38i	−0.285943	+	0.285943i
$913$	3976.35	−	1581.95i	0.144138	−	0.0573437i
$914$		−	12297.9i		−	0.445054i
$915$	60242.6	−	60242.6i	2.17657	−	2.17657i
$916$	219.845	+	219.845i	0.00793000	+	0.00793000i
$917$	−1520.44	+	1520.44i	−0.0547540	+	0.0547540i
$918$	−24948.2	+	24948.2i	−0.896963	+	0.896963i
$919$		−	11022.1i		−	0.395630i	−0.980239	−	0.197815i	$-0.936615\pi$
$919$		−	11022.1i		−	0.395630i	0.980239	−	0.197815i	$-0.0633846\pi$
$920$	−50150.0			−1.79717
$921$	14882.7	+	14882.7i	0.532467	+	0.532467i
$922$			6717.85i			0.239957i
$923$	−21286.5	+	24990.7i	−0.759104	+	0.891202i
$924$	6787.78	−	2700.44i	0.241668	−	0.0961450i
$925$	46186.4	+	46186.4i	1.64173	+	1.64173i
$926$			17238.2i			0.611752i
$927$			9772.80i			0.346258i
$928$	−4543.22	−	4543.22i	−0.160710	−	0.160710i
$929$	−6055.01	−	6055.01i	−0.213841	−	0.213841i	0.592056	−	0.805897i	$-0.298317\pi$
$929$	−6055.01	−	6055.01i	−0.213841	−	0.213841i	−0.805897	+	0.592056i	$0.798317\pi$
$930$	−18952.2	−	18952.2i	−0.668244	−	0.668244i
$931$	−8591.13	−	8591.13i	−0.302431	−	0.302431i
$932$		−	9636.10i		−	0.338671i
$933$		−	36004.0i		−	1.26336i
$934$	14870.8	+	14870.8i	0.520973	+	0.520973i
$935$	−30782.6	−	77374.5i	−1.07668	−	2.70633i
$936$	31885.1	−	37433.7i	1.11346	−	1.30722i
$937$			9273.46i			0.323320i	0.986847	+	0.161660i	$0.0516848\pi$
$937$			9273.46i			0.323320i	−0.986847	+	0.161660i	$0.948315\pi$
$938$	6551.50	+	6551.50i	0.228053	+	0.228053i
$939$	−33830.1			−1.17572
$940$			29263.8i			1.01541i
$941$	1763.82	−	1763.82i	0.0611040	−	0.0611040i	−0.675894	−	0.736998i	$-0.736242\pi$
$941$	1763.82	−	1763.82i	0.0611040	−	0.0611040i	0.736998	+	0.675894i	$0.236242\pi$
$942$	−44325.8	+	44325.8i	−1.53313	+	1.53313i
$943$	12009.0	+	12009.0i	0.414703	+	0.414703i
$944$	10760.5	−	10760.5i	0.371002	−	0.371002i
$945$		−	19598.6i		−	0.674650i
$946$	−12402.5	+	4934.21i	−0.426259	+	0.169582i
$947$	−7686.43	+	7686.43i	−0.263755	+	0.263755i	−0.826577	−	0.562823i	$-0.809715\pi$
$947$	−7686.43	+	7686.43i	−0.263755	+	0.263755i	0.562823	+	0.826577i	$0.309715\pi$
$948$	19670.5			0.673911
$949$	35385.8	−	41543.5i	1.21040	−	1.42103i
$950$	−22390.5			−0.764677
$951$	−30220.4	−	30220.4i	−1.03046	−	1.03046i
$952$		−	23640.9i		−	0.804840i
$953$	50202.7			1.70643			0.853214	−	0.521561i	$-0.174650\pi$
$953$	50202.7			1.70643			0.853214	+	0.521561i	$0.174650\pi$
$954$	1249.54	−	1249.54i	0.0424060	−	0.0424060i
$955$	17559.0	+	17559.0i	0.594971	+	0.594971i
$956$	319.781	+	319.781i	0.0108185	+	0.0108185i
$957$	6040.29	−	14021.7i	0.204028	−	0.473624i
$958$	12149.5			0.409743
$959$	8944.85			0.301193
$960$	−59231.6	+	59231.6i	−1.99135	+	1.99135i
$961$		−	23976.6i		−	0.804826i
$962$	−29476.6	+	2359.44i	−0.987904	+	0.0790762i
$963$		−	3538.63i		−	0.118412i
$964$	−8625.41	+	8625.41i	−0.288180	+	0.288180i
$965$			55164.6i			1.84022i
$966$		−	15998.2i		−	0.532851i
$967$	31306.6	−	31306.6i	1.04111	−	1.04111i	0.0419900	−	0.999118i	$-0.486630\pi$
$967$	31306.6	−	31306.6i	1.04111	−	1.04111i	0.999118	−	0.0419900i	$-0.0133698\pi$
$968$	920.130	−	32719.6i	0.0305518	−	1.08641i
$969$	30993.7	−	30993.7i	1.02751	−	1.02751i
$970$	4385.69	+	4385.69i	0.145171	+	0.145171i
$971$	−38389.0			−1.26876			−0.634378	−	0.773023i	$-0.718744\pi$
$971$	−38389.0			−1.26876			−0.634378	+	0.773023i	$0.718744\pi$
$972$			12189.9i			0.402254i
$973$	5093.80	−	5093.80i	0.167831	−	0.167831i
$974$	−25572.2			−0.841258
$975$	90107.4	−	7212.59i	2.95974	−	0.236911i
$976$		−	16626.8i		−	0.545298i
$977$	−8487.20	−	8487.20i	−0.277922	−	0.277922i	0.554357	−	0.832279i	$-0.312964\pi$
$977$	−8487.20	−	8487.20i	−0.277922	−	0.277922i	−0.832279	+	0.554357i	$0.812964\pi$
$978$		−	45500.3i		−	1.48767i
$979$	−3878.75	+	1543.12i	−0.126625	+	0.0503762i
$980$	−11272.1	−	11272.1i	−0.367423	−	0.367423i
$981$	−53888.7	+	53888.7i	−1.75386	+	1.75386i
$982$	516.223	−	516.223i	0.0167753	−	0.0167753i
$983$	−29302.5	+	29302.5i	−0.950767	+	0.950767i	−0.998844	−	0.0480763i	$-0.984691\pi$
$983$	−29302.5	+	29302.5i	−0.950767	+	0.950767i	0.0480763	+	0.998844i	$0.484691\pi$
$984$	32255.7			1.04499
$985$	26779.5			0.866261
$986$	−9571.64	−	9571.64i	−0.309151	−	0.309151i
$987$	−34074.3			−1.09888
$988$	−3983.58	+	4676.80i	−0.128274	+	0.150596i
$989$		−	17715.9i		−	0.569599i
$990$	−60195.7	−	25931.1i	−1.93247	−	0.832469i
$991$	−13640.8			−0.437249			−0.218625	−	0.975809i	$-0.570157\pi$
$991$	−13640.8			−0.437249			−0.218625	+	0.975809i	$0.570157\pi$
$992$	9771.09			0.312734
$993$	64.1387	+	64.1387i	0.00204973	+	0.00204973i
$994$	8783.97	+	8783.97i	0.280292	+	0.280292i
$995$	−57461.6	+	57461.6i	−1.83081	+	1.83081i
$996$	2089.85	+	2089.85i	0.0664853	+	0.0664853i
$997$			42661.1i			1.35516i	0.735451	+	0.677578i	$0.236971\pi$
$997$			42661.1i			1.35516i	−0.735451	+	0.677578i	$0.763029\pi$
$998$	28557.1			0.905771
$999$	−26122.2	+	26122.2i	−0.827298	+	0.827298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.14	✓	80
11.10	odd	2	inner	143.4.g.a.21.27	yes	80
13.5	odd	4	inner	143.4.g.a.109.27	yes	80
143.109	even	4	inner	143.4.g.a.109.14	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.14	✓	80	1.1	even	1	trivial
143.4.g.a.21.27	yes	80	11.10	odd	2	inner
143.4.g.a.109.14	yes	80	143.109	even	4	inner
143.4.g.a.109.27	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)

\(f(q)\)	\(=\)	\(q+(-1.57816 + 1.57816i) q^{2} -8.34617 q^{3} +3.01884i q^{4} +(-13.3430 - 13.3430i) q^{5} +(13.1716 - 13.1716i) q^{6} +(-5.61955 - 5.61955i) q^{7} +(-17.3895 - 17.3895i) q^{8} +42.6586 q^{9} +O(q^{10})\)	\(q+(-1.57816 + 1.57816i) q^{2} -8.34617 q^{3} +3.01884i q^{4} +(-13.3430 - 13.3430i) q^{5} +(13.1716 - 13.1716i) q^{6} +(-5.61955 - 5.61955i) q^{7} +(-17.3895 - 17.3895i) q^{8} +42.6586 q^{9} +42.1147 q^{10} +(-33.5062 - 14.4338i) q^{11} -25.1958i q^{12} +(3.73989 + 46.7227i) q^{13} +17.7371 q^{14} +(111.363 + 111.363i) q^{15} +30.7359 q^{16} -120.961 q^{17} +(-67.3220 + 67.3220i) q^{18} +(30.7000 - 30.7000i) q^{19} +(40.2804 - 40.2804i) q^{20} +(46.9018 + 46.9018i) q^{21} +(75.6568 - 30.0992i) q^{22} +108.069i q^{23} +(145.135 + 145.135i) q^{24} +231.071i q^{25} +(-79.6379 - 67.8337i) q^{26} -130.690 q^{27} +(16.9645 - 16.9645i) q^{28} -50.1406i q^{29} -351.496 q^{30} +(53.9186 + 53.9186i) q^{31} +(90.6097 - 90.6097i) q^{32} +(279.649 + 120.467i) q^{33} +(190.896 - 190.896i) q^{34} +149.963i q^{35} +128.780i q^{36} +(199.880 - 199.880i) q^{37} +96.8989i q^{38} +(-31.2138 - 389.956i) q^{39} +464.055i q^{40} +(111.123 - 111.123i) q^{41} -148.037 q^{42} -163.931 q^{43} +(43.5734 - 101.150i) q^{44} +(-569.194 - 569.194i) q^{45} +(-170.550 - 170.550i) q^{46} +(-363.252 + 363.252i) q^{47} -256.527 q^{48} -279.841i q^{49} +(-364.666 - 364.666i) q^{50} +1009.57 q^{51} +(-141.048 + 11.2901i) q^{52} -18.5606 q^{53} +(206.249 - 206.249i) q^{54} +(254.483 + 639.663i) q^{55} +195.442i q^{56} +(-256.228 + 256.228i) q^{57} +(79.1297 + 79.1297i) q^{58} +(350.097 - 350.097i) q^{59} +(-336.187 + 336.187i) q^{60} -540.958i q^{61} -170.184 q^{62} +(-239.722 - 239.722i) q^{63} +531.879i q^{64} +(573.519 - 673.322i) q^{65} +(-631.445 + 251.213i) q^{66} +(369.368 + 369.368i) q^{67} -365.163i q^{68} -901.964i q^{69} +(-236.666 - 236.666i) q^{70} +(495.232 + 495.232i) q^{71} +(-741.811 - 741.811i) q^{72} +(-823.253 - 823.253i) q^{73} +630.884i q^{74} -1928.56i q^{75} +(92.6785 + 92.6785i) q^{76} +(107.178 + 269.401i) q^{77} +(664.672 + 566.152i) q^{78} +780.706i q^{79} +(-410.108 - 410.108i) q^{80} -61.0243 q^{81} +350.738i q^{82} +(-82.9443 + 82.9443i) q^{83} +(-141.589 + 141.589i) q^{84} +(1613.99 + 1613.99i) q^{85} +(258.709 - 258.709i) q^{86} +418.482i q^{87} +(331.659 + 833.651i) q^{88} +(80.9085 - 80.9085i) q^{89} +1796.55 q^{90} +(241.544 - 283.577i) q^{91} -326.244 q^{92} +(-450.014 - 450.014i) q^{93} -1146.54i q^{94} -819.260 q^{95} +(-756.244 + 756.244i) q^{96} +(104.137 + 104.137i) q^{97} +(441.633 + 441.633i) q^{98} +(-1429.33 - 615.726i) 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

Properties

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