LMFDB - Embedded newform 143.4.g.a.21.6

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			21.6
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.94074 + 2.94074i) q^{2} +7.57281 q^{3} -9.29587i q^{4} +(4.79920 + 4.79920i) q^{5} +(-22.2696 + 22.2696i) q^{6} +(1.82819 + 1.82819i) q^{7} +(3.81081 + 3.81081i) q^{8} +30.3474 q^{9} +O(q^{10})$	\(q+(-2.94074 + 2.94074i) q^{2} +7.57281 q^{3} -9.29587i q^{4} +(4.79920 + 4.79920i) q^{5} +(-22.2696 + 22.2696i) q^{6} +(1.82819 + 1.82819i) q^{7} +(3.81081 + 3.81081i) q^{8} +30.3474 q^{9} -28.2264 q^{10} +(-23.8618 + 27.5973i) q^{11} -70.3958i q^{12} +(1.30280 + 46.8541i) q^{13} -10.7524 q^{14} +(36.3434 + 36.3434i) q^{15} +51.9538 q^{16} +133.917 q^{17} +(-89.2437 + 89.2437i) q^{18} +(-33.0896 + 33.0896i) q^{19} +(44.6128 - 44.6128i) q^{20} +(13.8445 + 13.8445i) q^{21} +(-10.9850 - 151.328i) q^{22} +177.922i q^{23} +(28.8586 + 28.8586i) q^{24} -78.9353i q^{25} +(-141.617 - 133.954i) q^{26} +25.3493 q^{27} +(16.9946 - 16.9946i) q^{28} -0.548976i q^{29} -213.753 q^{30} +(-79.1825 - 79.1825i) q^{31} +(-183.269 + 183.269i) q^{32} +(-180.701 + 208.989i) q^{33} +(-393.814 + 393.814i) q^{34} +17.5477i q^{35} -282.106i q^{36} +(-104.409 + 104.409i) q^{37} -194.616i q^{38} +(9.86582 + 354.817i) q^{39} +36.5777i q^{40} +(197.476 - 197.476i) q^{41} -81.4262 q^{42} -267.294 q^{43} +(256.541 + 221.817i) q^{44} +(145.643 + 145.643i) q^{45} +(-523.220 - 523.220i) q^{46} +(168.175 - 168.175i) q^{47} +393.436 q^{48} -336.315i q^{49} +(232.128 + 232.128i) q^{50} +1014.13 q^{51} +(435.549 - 12.1106i) q^{52} +429.707 q^{53} +(-74.5455 + 74.5455i) q^{54} +(-246.963 + 17.9273i) q^{55} +13.9338i q^{56} +(-250.582 + 250.582i) q^{57} +(1.61439 + 1.61439i) q^{58} +(43.5985 - 43.5985i) q^{59} +(337.844 - 337.844i) q^{60} -256.599i q^{61} +465.710 q^{62} +(55.4808 + 55.4808i) q^{63} -662.261i q^{64} +(-218.610 + 231.115i) q^{65} +(-83.1876 - 1145.98i) q^{66} +(597.966 + 597.966i) q^{67} -1244.87i q^{68} +1347.37i q^{69} +(-51.6032 - 51.6032i) q^{70} +(32.2498 + 32.2498i) q^{71} +(115.648 + 115.648i) q^{72} +(-345.749 - 345.749i) q^{73} -614.082i q^{74} -597.762i q^{75} +(307.597 + 307.597i) q^{76} +(-94.0771 + 6.82915i) q^{77} +(-1072.44 - 1014.41i) q^{78} -655.816i q^{79} +(249.337 + 249.337i) q^{80} -627.415 q^{81} +1161.45i q^{82} +(203.541 - 203.541i) q^{83} +(128.697 - 128.697i) q^{84} +(642.694 + 642.694i) q^{85} +(786.042 - 786.042i) q^{86} -4.15729i q^{87} +(-196.101 + 14.2352i) q^{88} +(708.463 - 708.463i) q^{89} -856.598 q^{90} +(-83.2763 + 88.0398i) q^{91} +1653.94 q^{92} +(-599.634 - 599.634i) q^{93} +989.116i q^{94} -317.608 q^{95} +(-1387.86 + 1387.86i) q^{96} +(287.138 + 287.138i) q^{97} +(989.015 + 989.015i) q^{98} +(-724.145 + 837.507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.94074	+	2.94074i	−1.03971	+	1.03971i	−0.0405292	+	0.999178i	$0.512904\pi$
$2$	−2.94074	+	2.94074i	−1.03971	+	1.03971i	−0.999178	+	0.0405292i	$0.987096\pi$
$3$	7.57281			1.45739			0.728694	−	0.684840i	$-0.240128\pi$
$3$	7.57281			1.45739			0.728694	+	0.684840i	$0.240128\pi$
$4$		−	9.29587i		−	1.16198i
$5$	4.79920	+	4.79920i	0.429254	+	0.429254i	0.888374	−	0.459120i	$-0.151835\pi$
$5$	4.79920	+	4.79920i	0.429254	+	0.429254i	−0.459120	+	0.888374i	$0.651835\pi$
$6$	−22.2696	+	22.2696i	−1.51526	+	1.51526i
$7$	1.82819	+	1.82819i	0.0987129	+	0.0987129i	0.754739	−	0.656026i	$-0.227764\pi$
$7$	1.82819	+	1.82819i	0.0987129	+	0.0987129i	−0.656026	+	0.754739i	$0.727764\pi$
$8$	3.81081	+	3.81081i	0.168416	+	0.168416i
$9$	30.3474			1.12398
$10$	−28.2264			−0.892597
$11$	−23.8618	+	27.5973i	−0.654056	+	0.756446i
$11$	−23.8618	+	27.5973i	−0.654056	+	0.756446i
$12$		−	70.3958i		−	1.69346i
$13$	1.30280	+	46.8541i	0.0277946	+	0.999614i
$13$	1.30280	+	46.8541i	0.0277946	+	0.999614i
$14$	−10.7524			−0.205265
$15$	36.3434	+	36.3434i	0.625589	+	0.625589i
$16$	51.9538			0.811777
$17$	133.917			1.91056			0.955282	−	0.295696i	$-0.0955516\pi$
$17$	133.917			1.91056			0.955282	+	0.295696i	$0.0955516\pi$
$18$	−89.2437	+	89.2437i	−1.16861	+	1.16861i
$19$	−33.0896	+	33.0896i	−0.399541	+	0.399541i	−0.878071	−	0.478530i	$-0.841170\pi$
$19$	−33.0896	+	33.0896i	−0.399541	+	0.399541i	0.478530	+	0.878071i	$0.341170\pi$
$20$	44.6128	−	44.6128i	0.498786	−	0.498786i
$21$	13.8445	+	13.8445i	0.143863	+	0.143863i
$22$	−10.9850	−	151.328i	−0.106455	−	1.46651i
$23$			177.922i			1.61301i	0.591228	+	0.806504i	$0.298643\pi$
$23$			177.922i			1.61301i	−0.591228	+	0.806504i	$0.701357\pi$
$24$	28.8586	+	28.8586i	0.245447	+	0.245447i
$25$		−	78.9353i		−	0.631482i
$26$	−141.617	−	133.954i	−1.06820	−	1.01041i
$27$	25.3493			0.180684
$28$	16.9946	−	16.9946i	0.114703	−	0.114703i
$29$		−	0.548976i		−	0.00351525i	−0.999998	−	0.00175763i	$-0.999441\pi$
$29$		−	0.548976i		−	0.00351525i	0.999998	−	0.00175763i	$-0.000559470\pi$
$30$	−213.753			−1.30086
$31$	−79.1825	−	79.1825i	−0.458761	−	0.458761i	0.439487	−	0.898249i	$-0.355160\pi$
$31$	−79.1825	−	79.1825i	−0.458761	−	0.458761i	−0.898249	+	0.439487i	$0.855160\pi$
$32$	−183.269	+	183.269i	−1.01243	+	1.01243i
$33$	−180.701	+	208.989i	−0.953213	+	1.10243i
$34$	−393.814	+	393.814i	−1.98643	+	1.98643i
$35$			17.5477i			0.0847458i
$36$		−	282.106i		−	1.30604i
$37$	−104.409	+	104.409i	−0.463914	+	0.463914i	−0.899936	−	0.436022i	$-0.856387\pi$
$37$	−104.409	+	104.409i	−0.463914	+	0.463914i	0.436022	+	0.899936i	$0.356387\pi$
$38$		−	194.616i		−	0.830812i
$39$	9.86582	+	354.817i	0.0405076	+	1.45682i
$40$			36.5777i			0.144586i
$41$	197.476	−	197.476i	0.752208	−	0.752208i	−0.222683	−	0.974891i	$-0.571481\pi$
$41$	197.476	−	197.476i	0.752208	−	0.752208i	0.974891	+	0.222683i	$0.0714815\pi$
$42$	−81.4262			−0.299151
$43$	−267.294			−0.947953			−0.473976	−	0.880538i	$-0.657182\pi$
$43$	−267.294			−0.947953			−0.473976	+	0.880538i	$0.657182\pi$
$44$	256.541	+	221.817i	0.878978	+	0.760003i
$45$	145.643	+	145.643i	0.482472	+	0.482472i
$46$	−523.220	−	523.220i	−1.67706	−	1.67706i
$47$	168.175	−	168.175i	0.521932	−	0.521932i	−0.396222	−	0.918155i	$-0.629679\pi$
$47$	168.175	−	168.175i	0.521932	−	0.521932i	0.918155	+	0.396222i	$0.129679\pi$
$48$	393.436			1.18307
$49$		−	336.315i		−	0.980512i
$50$	232.128	+	232.128i	0.656557	+	0.656557i
$51$	1014.13			2.78443
$52$	435.549	−	12.1106i	1.16153	−	0.0322969i
$53$	429.707			1.11367			0.556837	−	0.830622i	$-0.312015\pi$
$53$	429.707			1.11367			0.556837	+	0.830622i	$0.312015\pi$
$54$	−74.5455	+	74.5455i	−0.187859	+	0.187859i
$55$	−246.963	+	17.9273i	−0.605463	+	0.0439512i
$56$			13.9338i			0.0332496i
$57$	−250.582	+	250.582i	−0.582287	+	0.582287i
$58$	1.61439	+	1.61439i	0.00365483	+	0.00365483i
$59$	43.5985	−	43.5985i	0.0962041	−	0.0962041i	−0.657367	−	0.753571i	$-0.728330\pi$
$59$	43.5985	−	43.5985i	0.0962041	−	0.0962041i	0.753571	+	0.657367i	$0.228330\pi$
$60$	337.844	−	337.844i	0.726924	−	0.726924i
$61$		−	256.599i		−	0.538593i	−0.963057	−	0.269296i	$-0.913209\pi$
$61$		−	256.599i		−	0.538593i	0.963057	−	0.269296i	$-0.0867911\pi$
$62$	465.710			0.953955
$63$	55.4808	+	55.4808i	0.110951	+	0.110951i
$64$		−	662.261i		−	1.29348i
$65$	−218.610	+	231.115i	−0.417157	+	0.441019i
$66$	−83.1876	−	1145.98i	−0.155147	−	2.13727i
$67$	597.966	+	597.966i	1.09035	+	1.09035i	0.995491	+	0.0948543i	$0.0302385\pi$
$67$	597.966	+	597.966i	1.09035	+	1.09035i	0.0948543	+	0.995491i	$0.469761\pi$
$68$		−	1244.87i		−	2.22004i
$69$			1347.37i			2.35078i
$70$	−51.6032	−	51.6032i	−0.0881108	−	0.0881108i
$71$	32.2498	+	32.2498i	0.0539062	+	0.0539062i	0.733546	−	0.679640i	$-0.237864\pi$
$71$	32.2498	+	32.2498i	0.0539062	+	0.0539062i	−0.679640	+	0.733546i	$0.737864\pi$
$72$	115.648	+	115.648i	0.189296	+	0.189296i
$73$	−345.749	−	345.749i	−0.554341	−	0.554341i	0.373350	−	0.927691i	$-0.378209\pi$
$73$	−345.749	−	345.749i	−0.554341	−	0.554341i	−0.927691	+	0.373350i	$0.878209\pi$
$74$		−	614.082i		−	0.964669i
$75$		−	597.762i		−	0.920315i
$76$	307.597	+	307.597i	0.464261	+	0.464261i
$77$	−94.0771	+	6.82915i	−0.139235	+	0.0101072i
$78$	−1072.44	−	1014.41i	−1.55679	−	1.47256i
$79$		−	655.816i		−	0.933988i	−0.884261	−	0.466994i	$-0.845337\pi$
$79$		−	655.816i		−	0.933988i	0.884261	−	0.466994i	$-0.154663\pi$
$80$	249.337	+	249.337i	0.348459	+	0.348459i
$81$	−627.415			−0.860651
$82$			1161.45i			1.56415i
$83$	203.541	−	203.541i	0.269175	−	0.269175i	−0.559593	−	0.828768i	$-0.689042\pi$
$83$	203.541	−	203.541i	0.269175	−	0.269175i	0.828768	+	0.559593i	$0.189042\pi$
$84$	128.697	−	128.697i	0.167166	−	0.167166i
$85$	642.694	+	642.694i	0.820117	+	0.820117i
$86$	786.042	−	786.042i	0.985594	−	0.985594i
$87$		−	4.15729i		−	0.00512308i
$88$	−196.101	+	14.2352i	−0.237551	+	0.0172441i
$89$	708.463	−	708.463i	0.843785	−	0.843785i	−0.145564	−	0.989349i	$-0.546500\pi$
$89$	708.463	−	708.463i	0.843785	−	0.843785i	0.989349	+	0.145564i	$0.0464996\pi$
$90$	−856.598			−1.00326
$91$	−83.2763	+	88.0398i	−0.0959311	+	0.101418i
$92$	1653.94			1.87429
$93$	−599.634	−	599.634i	−0.668593	−	0.668593i
$94$			989.116i			1.08531i
$95$	−317.608			−0.343009
$96$	−1387.86	+	1387.86i	−1.47550	+	1.47550i
$97$	287.138	+	287.138i	0.300561	+	0.300561i	0.841233	−	0.540672i	$-0.181830\pi$
$97$	287.138	+	287.138i	0.300561	+	0.300561i	−0.540672	+	0.841233i	$0.681830\pi$
$98$	989.015	+	989.015i	1.01945	+	1.01945i
$99$	−724.145	+	837.507i	−0.735145	+	0.850229i
$100$	−733.772			−0.733772
$101$	707.387			0.696907			0.348453	−	0.937326i	$-0.386707\pi$
$101$	707.387			0.696907			0.348453	+	0.937326i	$0.386707\pi$
$102$	−2982.28	+	2982.28i	−2.89500	+	2.89500i
$103$		−	1749.75i		−	1.67386i	−0.547308	−	0.836931i	$-0.684347\pi$
$103$		−	1749.75i		−	1.67386i	0.547308	−	0.836931i	$-0.315653\pi$
$104$	−173.587	+	183.517i	−0.163670	+	0.173032i
$105$			132.885i			0.123507i
$106$	−1263.65	+	1263.65i	−1.15790	+	1.15790i
$107$		−	456.072i		−	0.412058i	−0.978546	−	0.206029i	$-0.933946\pi$
$107$		−	456.072i		−	0.412058i	0.978546	−	0.206029i	$-0.0660541\pi$
$108$		−	235.643i		−	0.209952i
$109$	−1095.47	+	1095.47i	−0.962637	+	0.962637i	−0.999327	−	0.0366896i	$-0.988319\pi$
$109$	−1095.47	+	1095.47i	−0.962637	+	0.962637i	0.0366896	+	0.999327i	$0.488319\pi$
$110$	673.534	−	778.973i	0.583808	−	0.675201i
$111$	−790.673	+	790.673i	−0.676102	+	0.676102i
$112$	94.9813	+	94.9813i	0.0801329	+	0.0801329i
$113$	−809.298			−0.673737			−0.336869	−	0.941552i	$-0.609368\pi$
$113$	−809.298			−0.673737			−0.336869	+	0.941552i	$0.609368\pi$
$114$		−	1473.79i		−	1.21082i
$115$	−853.882	+	853.882i	−0.692390	+	0.692390i
$116$	−5.10321			−0.00408466
$117$	39.5365	+	1421.90i	0.0312406	+	1.12354i
$118$			256.424i			0.200048i
$119$	244.825	+	244.825i	0.188597	+	0.188597i
$120$			276.996i			0.210718i
$121$	−192.224	−	1317.05i	−0.144421	−	0.989516i
$122$	754.591	+	754.591i	0.559979	+	0.559979i
$123$	1495.45	−	1495.45i	1.09626	−	1.09626i
$124$	−736.070	+	736.070i	−0.533073	+	0.533073i
$125$	978.727	−	978.727i	0.700320	−	0.700320i
$126$	−326.309			−0.230713
$127$	2680.02			1.87255			0.936274	−	0.351270i	$-0.114250\pi$
$127$	2680.02			1.87255			0.936274	+	0.351270i	$0.114250\pi$
$128$	481.385	+	481.385i	0.332413	+	0.332413i
$129$	−2024.17			−1.38153
$130$	−36.7732	−	1322.52i	−0.0248094	−	0.892252i
$131$		−	334.647i		−	0.223193i	−0.993754	−	0.111596i	$-0.964404\pi$
$131$		−	334.647i		−	0.223193i	0.993754	−	0.111596i	$-0.0355963\pi$
$132$	1942.74	+	1679.77i	1.28101	+	1.10762i
$133$	−120.988			−0.0788798
$134$	−3516.92			−2.26728
$135$	121.656	+	121.656i	0.0775593	+	0.0775593i
$136$	510.332	+	510.332i	0.321769	+	0.321769i
$137$	764.065	−	764.065i	0.476485	−	0.476485i	−0.427521	−	0.904006i	$-0.640613\pi$
$137$	764.065	−	764.065i	0.476485	−	0.476485i	0.904006	+	0.427521i	$0.140613\pi$
$138$	−3962.25	−	3962.25i	−2.44412	−	2.44412i
$139$			2336.39i			1.42569i	0.701324	+	0.712843i	$0.252593\pi$
$139$			2336.39i			1.42569i	−0.701324	+	0.712843i	$0.747407\pi$
$140$	163.121			0.0984732
$141$	1273.56	−	1273.56i	0.760657	−	0.760657i
$142$	−189.676			−0.112093
$143$	−1324.13	−	1082.07i	−0.774333	−	0.632778i
$144$	1576.66			0.912420
$145$	2.63465	−	2.63465i	0.00150893	−	0.00150893i
$146$	2033.51			1.15270
$147$		−	2546.85i		−	1.42899i
$148$	970.577	+	970.577i	0.539060	+	0.539060i
$149$	−562.943	+	562.943i	−0.309517	+	0.309517i	−0.844722	−	0.535205i	$-0.820234\pi$
$149$	−562.943	+	562.943i	−0.309517	+	0.309517i	0.535205	+	0.844722i	$0.320234\pi$
$150$	1757.86	+	1757.86i	0.956858	+	0.956858i
$151$	436.625	+	436.625i	0.235311	+	0.235311i	0.814905	−	0.579594i	$-0.196789\pi$
$151$	436.625	+	436.625i	0.235311	+	0.235311i	−0.579594	+	0.814905i	$0.696789\pi$
$152$	−252.197			−0.134578
$153$	4064.03			2.14743
$154$	256.573	−	296.739i	0.134255	−	0.155272i
$155$		−	760.026i		−	0.393850i
$156$	3298.33	−	91.7114i	1.69281	−	0.0470691i
$157$	−2424.46			−1.23244			−0.616221	−	0.787573i	$-0.711337\pi$
$157$	−2424.46			−1.23244			−0.616221	+	0.787573i	$0.711337\pi$
$158$	1928.58	+	1928.58i	0.971074	+	0.971074i
$159$	3254.09			1.62305
$160$	−1759.09			−0.869176
$161$	−325.274	+	325.274i	−0.159225	+	0.159225i
$162$	1845.06	−	1845.06i	0.894826	−	0.894826i
$163$	1706.18	−	1706.18i	0.819867	−	0.819867i	−0.166221	−	0.986089i	$-0.553157\pi$
$163$	1706.18	−	1706.18i	0.819867	−	0.819867i	0.986089	+	0.166221i	$0.0531566\pi$
$164$	−1835.71	−	1835.71i	−0.874053	−	0.874053i
$165$	−1870.20	+	135.760i	−0.882395	+	0.0640539i
$166$			1197.12i			0.559727i
$167$	219.071	+	219.071i	0.101510	+	0.101510i	0.756038	−	0.654528i	$-0.227133\pi$
$167$	219.071	+	219.071i	0.101510	+	0.101510i	−0.654528	+	0.756038i	$0.727133\pi$
$168$			105.518i			0.0484576i
$169$	−2193.61	+	122.082i	−0.998455	+	0.0555678i
$170$	−3779.99			−1.70536
$171$	−1004.19	+	1004.19i	−0.449076	+	0.449076i
$172$			2484.73i			1.10151i
$173$	1488.76			0.654268			0.327134	−	0.944978i	$-0.393917\pi$
$173$	1488.76			0.654268			0.327134	+	0.944978i	$0.393917\pi$
$174$	12.2255	+	12.2255i	0.00532651	+	0.00532651i
$175$	144.309	−	144.309i	0.0623355	−	0.0623355i
$176$	−1239.71	+	1433.78i	−0.530948	+	0.614066i
$177$	330.163	−	330.163i	0.140207	−	0.140207i
$178$			4166.80i			1.75458i
$179$			1453.71i			0.607014i	0.952829	+	0.303507i	$0.0981576\pi$
$179$			1453.71i			0.607014i	−0.952829	+	0.303507i	$0.901842\pi$
$180$	1353.88	−	1353.88i	0.560624	−	0.560624i
$181$			2841.03i			1.16670i	0.812223	+	0.583348i	$0.198257\pi$
$181$			2841.03i			1.16670i	−0.812223	+	0.583348i	$0.801743\pi$
$182$	−14.0082	−	503.796i	−0.00570527	−	0.205186i
$183$		−	1943.18i		−	0.784938i
$184$	−678.026	+	678.026i	−0.271656	+	0.271656i
$185$	−1002.16			−0.398273
$186$	3526.73			1.39028
$187$	−3195.50	+	3695.74i	−1.24962	+	1.44524i
$188$	−1563.33	−	1563.33i	−0.606477	−	0.606477i
$189$	46.3432	+	46.3432i	0.0178358	+	0.0178358i
$190$	934.001	−	934.001i	0.356629	−	0.356629i
$191$	−2788.53			−1.05639			−0.528195	−	0.849123i	$-0.677131\pi$
$191$	−2788.53			−1.05639			−0.528195	+	0.849123i	$0.677131\pi$
$192$		−	5015.17i		−	1.88510i
$193$	−1907.03	−	1907.03i	−0.711248	−	0.711248i	0.255548	−	0.966796i	$-0.417744\pi$
$193$	−1907.03	−	1907.03i	−0.711248	−	0.711248i	−0.966796	+	0.255548i	$0.917744\pi$
$194$	−1688.79			−0.624991
$195$	−1655.49	+	1750.19i	−0.607959	+	0.642735i
$196$	−3126.34			−1.13934
$197$	2500.42	−	2500.42i	0.904304	−	0.904304i	−0.0915011	−	0.995805i	$-0.529167\pi$
$197$	2500.42	−	2500.42i	0.904304	−	0.904304i	0.995805	+	0.0915011i	$0.0291665\pi$
$198$	−333.368	−	4592.41i	−0.119654	−	1.64832i
$199$		−	629.975i		−	0.224411i	−0.993685	−	0.112205i	$-0.964209\pi$
$199$		−	629.975i		−	0.224411i	0.993685	−	0.112205i	$-0.0357915\pi$
$200$	300.808	−	300.808i	0.106352	−	0.106352i
$201$	4528.28	+	4528.28i	1.58906	+	1.58906i
$202$	−2080.24	+	2080.24i	−0.724579	+	0.724579i
$203$	1.00363	−	1.00363i	0.000347001	−	0.000347001i
$204$		−	9427.18i		−	3.23546i
$205$	1895.45			0.645776
$206$	5145.55	+	5145.55i	1.74033	+	1.74033i
$207$			5399.46i			1.81299i
$208$	67.6851	+	2434.24i	0.0225631	+	0.811464i
$209$	−123.605	−	1702.77i	−0.0409089	−	0.563554i
$210$	−390.781	−	390.781i	−0.128412	−	0.128412i
$211$		−	3090.42i		−	1.00831i	−0.863614	−	0.504154i	$-0.831804\pi$
$211$		−	3090.42i		−	1.00831i	0.863614	−	0.504154i	$-0.168196\pi$
$212$		−	3994.50i		−	1.29407i
$213$	244.221	+	244.221i	0.0785623	+	0.0785623i
$214$	1341.19	+	1341.19i	0.428420	+	0.428420i
$215$	−1282.80	−	1282.80i	−0.406912	−	0.406912i
$216$	96.6013	+	96.6013i	0.0304300	+	0.0304300i
$217$		−	289.521i		−	0.0905713i
$218$		−	6443.01i		−	2.00172i
$219$	−2618.29	−	2618.29i	−0.807889	−	0.807889i
$220$	166.650	+	2295.74i	0.0510706	+	0.703539i
$221$	174.466	+	6274.54i	0.0531034	+	1.90983i
$222$		−	4650.32i		−	1.40590i
$223$	−898.690	−	898.690i	−0.269869	−	0.269869i	0.559179	−	0.829047i	$-0.311117\pi$
$223$	−898.690	−	898.690i	−0.269869	−	0.269869i	−0.829047	+	0.559179i	$0.811117\pi$
$224$	−670.100			−0.199879
$225$		−	2395.48i		−	0.709772i
$226$	2379.93	−	2379.93i	0.700490	−	0.700490i
$227$	−2506.75	+	2506.75i	−0.732947	+	0.732947i	−0.971203	−	0.238255i	$-0.923424\pi$
$227$	−2506.75	+	2506.75i	−0.732947	+	0.732947i	0.238255	+	0.971203i	$0.423424\pi$
$228$	2329.37	+	2329.37i	0.676608	+	0.676608i
$229$	2502.97	−	2502.97i	0.722275	−	0.722275i	−0.246793	−	0.969068i	$-0.579377\pi$
$229$	2502.97	−	2502.97i	0.722275	−	0.722275i	0.969068	+	0.246793i	$0.0793767\pi$
$230$		−	5022.08i		−	1.43977i
$231$	−712.427	+	51.7158i	−0.202919	+	0.0147301i
$232$	2.09205	−	2.09205i	0.000592024	−	0.000592024i
$233$	4076.16			1.14609			0.573043	−	0.819526i	$-0.305763\pi$
$233$	4076.16			1.14609			0.573043	+	0.819526i	$0.305763\pi$
$234$	−4297.70	−	4065.17i	−1.20064	−	1.13568i
$235$	1614.21			0.448083
$236$	−405.286	−	405.286i	−0.111788	−	0.111788i
$237$		−	4966.36i		−	1.36118i
$238$	−1439.93			−0.392172
$239$	−2322.13	+	2322.13i	−0.628476	+	0.628476i	−0.947685	−	0.319208i	$-0.896583\pi$
$239$	−2322.13	+	2322.13i	−0.628476	+	0.628476i	0.319208	+	0.947685i	$0.396583\pi$
$240$	1888.18	+	1888.18i	0.507839	+	0.507839i
$241$	−3021.30	−	3021.30i	−0.807549	−	0.807549i	0.176714	−	0.984262i	$-0.443453\pi$
$241$	−3021.30	−	3021.30i	−0.807549	−	0.807549i	−0.984262	+	0.176714i	$0.943453\pi$
$242$	4438.37	+	3307.81i	1.17896	+	0.878652i
$243$	−5435.72			−1.43499
$244$	−2385.31			−0.625836
$245$	1614.05	−	1614.05i	0.420888	−	0.420888i
$246$			8795.42i			2.27958i
$247$	−1593.49	−	1507.28i	−0.410492	−	0.388282i
$248$		−	603.500i		−	0.154525i
$249$	1541.38	−	1541.38i	0.392293	−	0.392293i
$250$			5756.36i			1.45626i
$251$			3074.29i			0.773098i	0.922269	+	0.386549i	$0.126333\pi$
$251$			3074.29i			0.773098i	−0.922269	+	0.386549i	$0.873667\pi$
$252$	515.742	−	515.742i	0.128923	−	0.128923i
$253$	−4910.16	−	4245.54i	−1.22015	−	1.05500i
$254$	−7881.25	+	7881.25i	−1.94690	+	1.94690i
$255$	4867.00	+	4867.00i	1.19523	+	1.19523i
$256$	2466.84			0.602255
$257$			3495.78i			0.848486i	0.905548	+	0.424243i	$0.139460\pi$
$257$			3495.78i			0.848486i	−0.905548	+	0.424243i	$0.860540\pi$
$258$	5952.54	−	5952.54i	1.43639	−	1.43639i
$259$	−381.760			−0.0915886
$260$	2148.41	+	2032.17i	0.512457	+	0.484730i
$261$		−	16.6600i		−	0.00395106i
$262$	984.108	+	984.108i	0.232055	+	0.232055i
$263$			5778.15i			1.35474i	0.735644	+	0.677369i	$0.236880\pi$
$263$			5778.15i			1.35474i	−0.735644	+	0.677369i	$0.763120\pi$
$264$	−1485.04	+	107.800i	−0.346204	+	0.0251313i
$265$	2062.25	+	2062.25i	0.478049	+	0.478049i
$266$	355.795	−	355.795i	0.0820119	−	0.0820119i
$267$	5365.05	−	5365.05i	1.22972	−	1.22972i
$268$	5558.61	−	5558.61i	1.26696	−	1.26696i
$269$	184.318			0.0417771			0.0208886	−	0.999782i	$-0.493350\pi$
$269$	184.318			0.0417771			0.0208886	+	0.999782i	$0.493350\pi$
$270$	−715.518			−0.161278
$271$	3100.04	+	3100.04i	0.694886	+	0.694886i	0.963303	−	0.268417i	$-0.0865003\pi$
$271$	3100.04	+	3100.04i	0.694886	+	0.694886i	−0.268417	+	0.963303i	$0.586500\pi$
$272$	6957.48			1.55095
$273$	−630.635	+	666.708i	−0.139809	+	0.147806i
$274$			4493.83i			0.990810i
$275$	2178.40	+	1883.54i	0.477682	+	0.413025i
$276$	12524.9			2.73157
$277$	−1517.49			−0.329160			−0.164580	−	0.986364i	$-0.552627\pi$
$277$	−1517.49			−0.329160			−0.164580	+	0.986364i	$0.552627\pi$
$278$	−6870.72	−	6870.72i	−1.48230	−	1.48230i
$279$	−2402.98	−	2402.98i	−0.515638	−	0.515638i
$280$	−66.8710	+	66.8710i	−0.0142725	+	0.0142725i
$281$	−4994.66	−	4994.66i	−1.06034	−	1.06034i	−0.998058	−	0.0622843i	$-0.980161\pi$
$281$	−4994.66	−	4994.66i	−1.06034	−	1.06034i	−0.0622843	−	0.998058i	$-0.519839\pi$
$282$			7490.38i			1.58172i
$283$	−9201.72			−1.93281			−0.966405	−	0.257023i	$-0.917258\pi$
$283$	−9201.72			−1.93281			−0.966405	+	0.257023i	$0.917258\pi$
$284$	299.790	−	299.790i	0.0626382	−	0.0626382i
$285$	−2405.18			−0.499897
$286$	7076.01	−	711.843i	1.46298	−	0.147175i
$287$	722.046			0.148505
$288$	−5561.73	+	5561.73i	−1.13795	+	1.13795i
$289$	13020.7			2.65026
$290$			15.4956i			0.00313770i
$291$	2174.44	+	2174.44i	0.438034	+	0.438034i
$292$	−3214.04	+	3214.04i	−0.644135	+	0.644135i
$293$	−6142.82	−	6142.82i	−1.22480	−	1.22480i	−0.965904	−	0.258899i	$-0.916640\pi$
$293$	−6142.82	−	6142.82i	−1.22480	−	1.22480i	−0.258899	−	0.965904i	$-0.583360\pi$
$294$	7489.62	+	7489.62i	1.48573	+	1.48573i
$295$	418.476			0.0825920
$296$	−795.770			−0.156261
$297$	−604.880	+	699.572i	−0.118177	+	0.136678i
$298$		−	3310.93i		−	0.643615i
$299$	−8336.35	+	231.795i	−1.61239	+	0.0448330i
$300$	−5556.72			−1.06939
$301$	−488.664	−	488.664i	−0.0935752	−	0.0935752i
$302$	−2568.00			−0.489310
$303$	5356.90			1.01566
$304$	−1719.13	+	1719.13i	−0.324339	+	0.324339i
$305$	1231.47	−	1231.47i	0.231193	−	0.231193i
$306$	−11951.2	+	11951.2i	−2.23270	+	2.23270i
$307$	−5061.39	−	5061.39i	−0.940941	−	0.940941i	0.0574094	−	0.998351i	$-0.481716\pi$
$307$	−5061.39	−	5061.39i	−0.940941	−	0.940941i	−0.998351	+	0.0574094i	$0.981716\pi$
$308$	63.4829	+	874.528i	0.0117444	+	0.161789i
$309$		−	13250.5i		−	2.43947i
$310$	2235.04	+	2235.04i	0.409489	+	0.409489i
$311$			2792.43i			0.509145i	0.967054	+	0.254573i	$0.0819348\pi$
$311$			2792.43i			0.509145i	−0.967054	+	0.254573i	$0.918065\pi$
$312$	−1314.54	+	1389.74i	−0.238530	+	0.252174i
$313$	−8167.74			−1.47498			−0.737489	−	0.675360i	$-0.763988\pi$
$313$	−8167.74			−1.47498			−0.737489	+	0.675360i	$0.763988\pi$
$314$	7129.71	−	7129.71i	1.28138	−	1.28138i
$315$			532.527i			0.0952524i
$316$	−6096.38			−1.08528
$317$	1784.65	+	1784.65i	0.316201	+	0.316201i	0.847306	−	0.531105i	$-0.178223\pi$
$317$	1784.65	+	1784.65i	0.316201	+	0.316201i	−0.531105	+	0.847306i	$0.678223\pi$
$318$	−9569.41	+	9569.41i	−1.68750	+	1.68750i
$319$	15.1503	+	13.0996i	0.00265910	+	0.00229917i
$320$	3178.32	−	3178.32i	0.555231	−	0.555231i
$321$		−	3453.75i		−	0.600528i
$322$		−	1913.09i		−	0.331094i
$323$	−4431.26	+	4431.26i	−0.763349	+	0.763349i
$324$			5832.37i			1.00006i
$325$	3698.44	−	102.837i	0.631238	−	0.0175518i
$326$			10034.9i			1.70484i
$327$	−8295.82	+	8295.82i	−1.40294	+	1.40294i
$328$	1505.09			0.253367
$329$	614.910			0.103043
$330$	5100.54	−	5899.01i	0.850835	−	0.984030i
$331$	−3695.29	−	3695.29i	−0.613629	−	0.613629i	0.330260	−	0.943890i	$-0.392863\pi$
$331$	−3695.29	−	3695.29i	−0.613629	−	0.613629i	−0.943890	+	0.330260i	$0.892863\pi$
$332$	−1892.09	−	1892.09i	−0.312777	−	0.312777i
$333$	−3168.56	+	3168.56i	−0.521429	+	0.521429i
$334$	−1288.46			−0.211082
$335$			5739.52i			0.936070i
$336$	719.275	+	719.275i	0.116785	+	0.116785i
$337$	6763.62			1.09329			0.546644	−	0.837365i	$-0.315905\pi$
$337$	6763.62			1.09329			0.546644	+	0.837365i	$0.315905\pi$
$338$	6091.80	−	6809.83i	0.980327	−	1.09588i
$339$	−6128.66			−0.981896
$340$	5974.40	−	5974.40i	0.952962	−	0.952962i
$341$	4074.67	−	295.784i	0.647084	−	0.0469725i
$342$		−	5906.09i		−	0.933815i
$343$	1241.92	−	1241.92i	0.195502	−	0.195502i
$344$	−1018.61	−	1018.61i	−0.159650	−	0.159650i
$345$	−6466.28	+	6466.28i	−1.00908	+	1.00908i
$346$	−4378.06	+	4378.06i	−0.680248	+	0.680248i
$347$			1684.10i			0.260539i	0.991479	+	0.130269i	$0.0415842\pi$
$347$			1684.10i			0.260539i	−0.991479	+	0.130269i	$0.958416\pi$
$348$	−38.6456			−0.00595294
$349$	−1273.03	−	1273.03i	−0.195254	−	0.195254i	0.602708	−	0.797962i	$-0.294088\pi$
$349$	−1273.03	−	1273.03i	−0.195254	−	0.195254i	−0.797962	+	0.602708i	$0.794088\pi$
$350$			848.747i			0.129621i
$351$	33.0249	+	1187.72i	0.00502205	+	0.180614i
$352$	−684.596	−	9430.86i	−0.103662	−	1.42803i
$353$	−3635.72	−	3635.72i	−0.548187	−	0.548187i	0.377729	−	0.925916i	$-0.376705\pi$
$353$	−3635.72	−	3635.72i	−0.548187	−	0.548187i	−0.925916	+	0.377729i	$0.876705\pi$
$354$			1941.85i			0.291548i
$355$			309.546i			0.0462789i
$356$	−6585.78	−	6585.78i	−0.980465	−	0.980465i
$357$	1854.01	+	1854.01i	0.274859	+	0.274859i
$358$	−4274.98	−	4274.98i	−0.631117	−	0.631117i
$359$	5908.29	+	5908.29i	0.868601	+	0.868601i	0.992318	−	0.123717i	$-0.0394815\pi$
$359$	5908.29	+	5908.29i	0.868601	+	0.868601i	−0.123717	+	0.992318i	$0.539481\pi$
$360$			1110.04i			0.162512i
$361$			4669.15i			0.680733i
$362$	−8354.71	−	8354.71i	−1.21302	−	1.21302i
$363$	−1455.68	−	9973.74i	−0.210477	−	1.44211i
$364$	818.407	+	774.126i	0.117847	+	0.111470i
$365$		−	3318.64i		−	0.475906i
$366$	5714.37	+	5714.37i	0.816106	+	0.816106i
$367$	3116.26			0.443235			0.221618	−	0.975134i	$-0.428866\pi$
$367$	3116.26			0.443235			0.221618	+	0.975134i	$0.428866\pi$
$368$			9243.69i			1.30940i
$369$	5992.88	−	5992.88i	0.845465	−	0.845465i
$370$	2947.10	−	2947.10i	0.414088	−	0.414088i
$371$	785.585	+	785.585i	0.109934	+	0.109934i
$372$	−5574.12	+	5574.12i	−0.776894	+	0.776894i
$373$			3835.38i			0.532408i	0.963917	+	0.266204i	$0.0857696\pi$
$373$			3835.38i			0.532408i	−0.963917	+	0.266204i	$0.914230\pi$
$374$	−1471.08	−	20265.3i	−0.203390	−	2.80186i
$375$	7411.71	−	7411.71i	1.02064	−	1.02064i
$376$	1281.77			0.175803
$377$	25.7218	−	0.715203i	0.00351389	−	9.77051e-5i
$378$	−272.567			−0.0370881
$379$	7564.93	+	7564.93i	1.02529	+	1.02529i	0.999672	+	0.0256163i	$0.00815481\pi$
$379$	7564.93	+	7564.93i	1.02529	+	1.02529i	0.0256163	+	0.999672i	$0.491845\pi$
$380$			2952.44i			0.398571i
$381$	20295.3			2.72903
$382$	8200.32	−	8200.32i	1.09834	−	1.09834i
$383$	−1072.27	−	1072.27i	−0.143056	−	0.143056i	0.631952	−	0.775008i	$-0.282254\pi$
$383$	−1072.27	−	1072.27i	−0.143056	−	0.143056i	−0.775008	+	0.631952i	$0.782254\pi$
$384$	3645.43	+	3645.43i	0.484454	+	0.484454i
$385$	−484.269	−	418.720i	−0.0641056	−	0.0554285i
$386$	11216.1			1.47898
$387$	−8111.68			−1.06548
$388$	2669.20	−	2669.20i	0.349247	−	0.349247i
$389$			7160.37i			0.933279i	0.884448	+	0.466639i	$0.154535\pi$
$389$			7160.37i			0.933279i	−0.884448	+	0.466639i	$0.845465\pi$
$390$	−278.476	−	10015.2i	−0.0361569	−	1.30036i
$391$			23826.7i			3.08176i
$392$	1281.64	−	1281.64i	0.165134	−	0.165134i
$393$		−	2534.21i		−	0.325278i
$394$			14706.2i			1.88042i
$395$	3147.39	−	3147.39i	0.400918	−	0.400918i
$396$	7785.36	+	6731.56i	0.987952	+	0.854226i
$397$	−561.423	+	561.423i	−0.0709748	+	0.0709748i	−0.741703	−	0.670728i	$-0.765982\pi$
$397$	−561.423	+	561.423i	−0.0709748	+	0.0709748i	0.670728	+	0.741703i	$0.265982\pi$
$398$	1852.59	+	1852.59i	0.233322	+	0.233322i
$399$	−916.221			−0.114958
$400$		−	4100.99i		−	0.512623i
$401$	−1202.86	+	1202.86i	−0.149796	+	0.149796i	−0.778027	−	0.628231i	$-0.783779\pi$
$401$	−1202.86	+	1202.86i	−0.149796	+	0.149796i	0.628231	+	0.778027i	$0.283779\pi$
$402$	−26633.0			−3.30431
$403$	3606.86	−	3813.18i	0.445833	−	0.471335i
$404$		−	6575.77i		−	0.809795i
$405$	−3011.09	−	3011.09i	−0.369438	−	0.369438i
$406$			5.90283i			0.000721558i
$407$	−390.019	−	5372.82i	−0.0475000	−	0.654351i
$408$	3864.65	+	3864.65i	0.468942	+	0.468942i
$409$	8654.68	−	8654.68i	1.04632	−	1.04632i	0.0474505	−	0.998874i	$-0.484890\pi$
$409$	8654.68	−	8654.68i	1.04632	−	1.04632i	0.998874	−	0.0474505i	$-0.0151096\pi$
$410$	−5574.03	+	5574.03i	−0.671418	+	0.671418i
$411$	5786.11	−	5786.11i	0.694423	−	0.694423i
$412$	−16265.4			−1.94500
$413$	159.413			0.0189932
$414$	−15878.4	−	15878.4i	−1.88498	−	1.88498i
$415$	1953.67			0.231089
$416$	−8825.65	−	8348.13i	−1.04018	−	0.983896i
$417$			17693.1i			2.07778i
$418$	5370.88	+	4643.90i	0.628465	+	0.543398i
$419$	−11526.3			−1.34390			−0.671950	−	0.740596i	$-0.734543\pi$
$419$	−11526.3			−1.34390			−0.671950	+	0.740596i	$0.734543\pi$
$420$	1235.28			0.143514
$421$	−4859.08	−	4859.08i	−0.562511	−	0.562511i	0.367509	−	0.930020i	$-0.380211\pi$
$421$	−4859.08	−	4859.08i	−0.562511	−	0.562511i	−0.930020	+	0.367509i	$0.880211\pi$
$422$	9088.11	+	9088.11i	1.04835	+	1.04835i
$423$	5103.67	−	5103.67i	0.586640	−	0.586640i
$424$	1637.53	+	1637.53i	0.187560	+	0.187560i
$425$		−	10570.8i		−	1.20649i
$426$	−1436.38			−0.163364
$427$	469.112	−	469.112i	0.0531661	−	0.0531661i
$428$	−4239.59			−0.478804
$429$	−10027.4	−	8194.31i	−1.12850	−	0.922203i
$430$	7544.75			0.846140
$431$	−5561.29	+	5561.29i	−0.621526	+	0.621526i	−0.945922	−	0.324395i	$-0.894839\pi$
$431$	−5561.29	+	5561.29i	−0.621526	+	0.621526i	0.324395	+	0.945922i	$0.394839\pi$
$432$	1316.99			0.146675
$433$		−	11916.7i		−	1.32259i	−0.750128	−	0.661293i	$-0.770008\pi$
$433$		−	11916.7i		−	1.32259i	0.750128	−	0.661293i	$-0.229992\pi$
$434$	851.406	+	851.406i	0.0941677	+	0.0941677i
$435$	19.9517	−	19.9517i	0.00219910	−	0.00219910i
$436$	10183.4	+	10183.4i	1.11857	+	1.11857i
$437$	−5887.36	−	5887.36i	−0.644464	−	0.644464i
$438$	15399.4			1.67994
$439$	14093.1			1.53218			0.766091	−	0.642732i	$-0.222199\pi$
$439$	14093.1			1.53218			0.766091	+	0.642732i	$0.222199\pi$
$440$	−1009.45	−	872.812i	−0.109372	−	0.0945675i
$441$		−	10206.3i		−	1.10207i
$442$	−18964.8	−	17938.7i	−2.04087	−	1.93045i
$443$	8200.16			0.879461			0.439731	−	0.898130i	$-0.355074\pi$
$443$	8200.16			0.879461			0.439731	+	0.898130i	$0.355074\pi$
$444$	7349.99	+	7349.99i	0.785620	+	0.785620i
$445$	6800.11			0.724396
$446$	5285.62			0.561169
$447$	−4263.06	+	4263.06i	−0.451087	+	0.451087i
$448$	1210.74	−	1210.74i	0.127683	−	0.127683i
$449$	−1743.69	+	1743.69i	−0.183273	+	0.183273i	−0.792780	−	0.609507i	$-0.791367\pi$
$449$	−1743.69	+	1743.69i	−0.183273	+	0.183273i	0.609507	+	0.792780i	$0.291367\pi$
$450$	7044.48	+	7044.48i	0.737956	+	0.737956i
$451$	737.665	+	10161.9i	0.0770184	+	1.06099i
$452$			7523.13i			0.782872i
$453$	3306.48	+	3306.48i	0.342940	+	0.342940i
$454$		−	14743.4i		−	1.52410i
$455$	−822.181	+	22.8611i	−0.0847130	+	0.00235548i
$456$	−1909.84			−0.196132
$457$	13322.5	−	13322.5i	1.36367	−	1.36367i	0.494486	−	0.869185i	$-0.335356\pi$
$457$	13322.5	−	13322.5i	1.36367	−	1.36367i	0.869185	−	0.494486i	$-0.164644\pi$
$458$			14721.2i			1.50191i
$459$	3394.69			0.345208
$460$	7937.57	+	7937.57i	0.804546	+	0.804546i
$461$	4560.70	−	4560.70i	0.460766	−	0.460766i	−0.438141	−	0.898906i	$-0.644363\pi$
$461$	4560.70	−	4560.70i	0.460766	−	0.460766i	0.898906	+	0.438141i	$0.144363\pi$
$462$	1942.98	−	2247.14i	0.195661	−	0.226291i
$463$	−6542.87	+	6542.87i	−0.656745	+	0.656745i	−0.954608	−	0.297864i	$-0.903726\pi$
$463$	−6542.87	+	6542.87i	−0.656745	+	0.656745i	0.297864	+	0.954608i	$0.403726\pi$
$464$		−	28.5214i		−	0.00285360i
$465$		−	5755.53i		−	0.573992i
$466$	−11986.9	+	11986.9i	−1.19159	+	1.19159i
$467$			1312.64i			0.130068i	0.997883	+	0.0650339i	$0.0207156\pi$
$467$			1312.64i			0.130068i	−0.997883	+	0.0650339i	$0.979284\pi$
$468$	13217.8	−	367.526i	1.30554	−	0.0363010i
$469$			2186.39i			0.215262i
$470$	−4746.97	+	4746.97i	−0.465875	+	0.465875i
$471$	−18360.0			−1.79614
$472$	332.292			0.0324046
$473$	6378.13	−	7376.60i	0.620014	−	0.717075i
$474$	14604.8	+	14604.8i	1.41523	+	1.41523i
$475$	2611.94	+	2611.94i	0.252303	+	0.252303i
$476$	2275.86	−	2275.86i	0.219147	−	0.219147i
$477$	13040.5			1.25175
$478$		−	13657.5i		−	1.30686i
$479$	6508.81	+	6508.81i	0.620867	+	0.620867i	0.945753	−	0.324886i	$-0.105326\pi$
$479$	6508.81	+	6508.81i	0.620867	+	0.620867i	−0.324886	+	0.945753i	$0.605326\pi$
$480$	−13321.2			−1.26673
$481$	−5028.03	−	4755.98i	−0.476629	−	0.450840i
$482$	17769.7			1.67923
$483$	−2463.24	+	2463.24i	−0.232052	+	0.232052i
$484$	−12243.1	+	1786.89i	−1.14980	+	0.167815i
$485$			2756.06i			0.258034i
$486$	15985.0	−	15985.0i	1.49197	−	1.49197i
$487$	−2640.00	−	2640.00i	−0.245646	−	0.245646i	0.573535	−	0.819181i	$-0.305572\pi$
$487$	−2640.00	−	2640.00i	−0.245646	−	0.245646i	−0.819181	+	0.573535i	$0.805572\pi$
$488$	977.852	−	977.852i	0.0907075	−	0.0907075i
$489$	12920.6	−	12920.6i	1.19486	−	1.19486i
$490$			9492.97i			0.875201i
$491$	−15621.8			−1.43585			−0.717924	−	0.696121i	$-0.754908\pi$
$491$	−15621.8			−1.43585			−0.717924	+	0.696121i	$0.754908\pi$
$492$	−13901.5	−	13901.5i	−1.27383	−	1.27383i
$493$		−	73.5171i		−	0.00671611i
$494$	9118.55	−	253.545i	0.830491	−	0.0230921i
$495$	−7494.69	+	544.047i	−0.680527	+	0.0494002i
$496$	−4113.83	−	4113.83i	−0.372412	−	0.372412i
$497$			117.917i			0.0106425i
$498$			9065.58i			0.815739i
$499$	5059.56	+	5059.56i	0.453901	+	0.453901i	0.896647	−	0.442746i	$-0.145996\pi$
$499$	5059.56	+	5059.56i	0.453901	+	0.453901i	−0.442746	+	0.896647i	$0.645996\pi$
$500$	−9098.12	−	9098.12i	−0.813760	−	0.813760i
$501$	1658.98	+	1658.98i	0.147940	+	0.147940i
$502$	−9040.68	−	9040.68i	−0.803795	−	0.803795i
$503$			13243.3i			1.17393i	0.809611	+	0.586967i	$0.199678\pi$
$503$			13243.3i			1.17393i	−0.809611	+	0.586967i	$0.800322\pi$
$504$			422.854i			0.0373718i
$505$	3394.89	+	3394.89i	0.299150	+	0.299150i
$506$	26924.5	−	1954.48i	2.36549	−	0.171714i
$507$	−16611.8	+	924.507i	−1.45514	+	0.0809838i
$508$		−	24913.2i		−	2.17587i
$509$	9420.28	+	9420.28i	0.820327	+	0.820327i	0.986155	−	0.165827i	$-0.0530295\pi$
$509$	9420.28	+	9420.28i	0.820327	+	0.820327i	−0.165827	+	0.986155i	$0.553029\pi$
$510$	−28625.1			−2.48538
$511$		−	1264.19i		−	0.109441i
$512$	−11105.4	+	11105.4i	−0.958582	+	0.958582i
$513$	−838.798	+	838.798i	−0.0721907	+	0.0721907i
$514$	−10280.2	−	10280.2i	−0.882177	−	0.882177i
$515$	8397.40	−	8397.40i	0.718512	−	0.718512i
$516$			18816.4i			1.60532i
$517$	628.212	+	8654.13i	0.0534405	+	0.736186i
$518$	1122.66	−	1122.66i	0.0952253	−	0.0952253i
$519$	11274.1			0.953522
$520$	−1713.82	+	47.6533i	−0.144530	+	0.00401872i
$521$	−10710.3			−0.900630			−0.450315	−	0.892870i	$-0.648688\pi$
$521$	−10710.3			−0.900630			−0.450315	+	0.892870i	$0.648688\pi$
$522$	48.9927	+	48.9927i	0.00410795	+	0.00410795i
$523$		−	7574.77i		−	0.633311i	−0.948541	−	0.316655i	$-0.897440\pi$
$523$		−	7574.77i		−	0.633311i	0.948541	−	0.316655i	$-0.102560\pi$
$524$	−3110.83			−0.259346
$525$	1092.82	−	1092.82i	0.0908469	−	0.0908469i
$526$	−16992.0	−	16992.0i	−1.40853	−	1.40853i
$527$	−10603.9	−	10603.9i	−0.876493	−	0.876493i
$528$	−9388.11	+	10857.8i	−0.773797	+	0.894932i
$529$	−19489.1			−1.60180
$530$	−12129.1			−0.994062
$531$	1323.10	−	1323.10i	0.108131	−	0.108131i
$532$			1124.69i			0.0916570i
$533$	9509.81	+	8995.27i	0.772825	+	0.731010i
$534$			31554.4i			2.55710i
$535$	2188.78	−	2188.78i	0.176877	−	0.176877i
$536$			4557.47i			0.367263i
$537$			11008.7i			0.884655i
$538$	−542.030	+	542.030i	−0.0434360	+	0.0434360i
$539$	9281.41	+	8025.11i	0.741704	+	0.641310i
$540$	1130.90	−	1130.90i	0.0901226	−	0.0901226i
$541$	13379.8	+	13379.8i	1.06329	+	1.06329i	0.997857	+	0.0654363i	$0.0208439\pi$
$541$	13379.8	+	13379.8i	1.06329	+	1.06329i	0.0654363	+	0.997857i	$0.479156\pi$
$542$	−18232.8			−1.44496
$543$			21514.5i			1.70033i
$544$	−24542.8	+	24542.8i	−1.93431	+	1.93431i
$545$	−10514.8			−0.826431
$546$	−106.082	−	3815.15i	−0.00831479	−	0.299035i
$547$			9938.16i			0.776828i	0.921485	+	0.388414i	$0.126977\pi$
$547$			9938.16i			0.776828i	−0.921485	+	0.388414i	$0.873023\pi$
$548$	−7102.65	−	7102.65i	−0.553668	−	0.553668i
$549$		−	7787.12i		−	0.605366i
$550$	−11945.1	+	867.108i	−0.926075	+	0.0672247i
$551$	18.1654	+	18.1654i	0.00140449	+	0.00140449i
$552$	−5134.56	+	5134.56i	−0.395908	+	0.395908i
$553$	1198.95	−	1198.95i	0.0921966	−	0.0921966i
$554$	4462.55	−	4462.55i	0.342230	−	0.342230i
$555$	−7589.20			−0.580439
$556$	21718.8			1.65662
$557$	3292.81	+	3292.81i	0.250486	+	0.250486i	0.821170	−	0.570684i	$-0.193322\pi$
$557$	3292.81	+	3292.81i	0.250486	+	0.250486i	−0.570684	+	0.821170i	$0.693322\pi$
$558$	14133.1			1.07222
$559$	−348.230	−	12523.8i	−0.0263480	−	0.947587i
$560$			911.669i			0.0687947i
$561$	−24198.9	+	27987.2i	−1.82118	+	2.10627i
$562$	29376.0			2.20489
$563$	−13441.8			−1.00622			−0.503112	−	0.864221i	$-0.667812\pi$
$563$	−13441.8			−1.00622			−0.503112	+	0.864221i	$0.667812\pi$
$564$	−11838.8	−	11838.8i	−0.883872	−	0.883872i
$565$	−3883.98	−	3883.98i	−0.289204	−	0.289204i
$566$	27059.8	−	27059.8i	2.00956	−	2.00956i
$567$	−1147.03	−	1147.03i	−0.0849574	−	0.0849574i
$568$			245.796i			0.0181573i
$569$	−11329.5			−0.834724			−0.417362	−	0.908740i	$-0.637045\pi$
$569$	−11329.5			−0.834724			−0.417362	+	0.908740i	$0.637045\pi$
$570$	7073.01	−	7073.01i	0.519747	−	0.519747i
$571$	−9713.39			−0.711896			−0.355948	−	0.934506i	$-0.615842\pi$
$571$	−9713.39			−0.711896			−0.355948	+	0.934506i	$0.615842\pi$
$572$	−10058.8	+	12309.0i	−0.735278	+	0.899762i
$573$	−21117.0			−1.53957
$574$	−2123.35	+	2123.35i	−0.154402	+	0.154402i
$575$	14044.3			1.01859
$576$		−	20097.9i		−	1.45384i
$577$	14108.5	+	14108.5i	1.01792	+	1.01792i	0.999836	+	0.0180883i	$0.00575801\pi$
$577$	14108.5	+	14108.5i	1.01792	+	1.01792i	0.0180883	+	0.999836i	$0.494242\pi$
$578$	−38290.5	+	38290.5i	−2.75549	+	2.75549i
$579$	−14441.6	−	14441.6i	−1.03656	−	1.03656i
$580$	−24.4913	−	24.4913i	−0.00175336	−	0.00175336i
$581$	744.223			0.0531422
$582$	−12788.9			−0.910854
$583$	−10253.6	+	11858.8i	−0.728406	+	0.842434i
$584$		−	2635.17i		−	0.186719i
$585$	−6634.24	+	7013.73i	−0.468875	+	0.495696i
$586$	36128.8			2.54687
$587$	−5300.02	−	5300.02i	−0.372666	−	0.372666i	0.495781	−	0.868447i	$-0.334882\pi$
$587$	−5300.02	−	5300.02i	−0.372666	−	0.372666i	−0.868447	+	0.495781i	$0.834882\pi$
$588$	−23675.2			−1.66046
$589$	5240.24			0.366588
$590$	−1230.63	+	1230.63i	−0.0858715	+	0.0858715i
$591$	18935.2	−	18935.2i	1.31792	−	1.31792i
$592$	−5424.46	+	5424.46i	−0.376595	+	0.376595i
$593$	14251.1	+	14251.1i	0.986887	+	0.986887i	0.999915	−	0.0130279i	$-0.00414701\pi$
$593$	14251.1	+	14251.1i	0.986887	+	0.986887i	−0.0130279	+	0.999915i	$0.504147\pi$
$594$	−278.463	−	3836.05i	−0.0192348	−	0.264975i
$595$			2349.93i			0.161912i
$596$	5233.05	+	5233.05i	0.359654	+	0.359654i
$597$		−	4770.68i		−	0.327053i
$598$	23833.4	−	25196.7i	1.62980	−	1.72302i
$599$	21440.1			1.46247			0.731234	−	0.682127i	$-0.238945\pi$
$599$	21440.1			1.46247			0.731234	+	0.682127i	$0.238945\pi$
$600$	2277.96	−	2277.96i	0.154995	−	0.154995i
$601$			11736.6i			0.796583i	0.917259	+	0.398291i	$0.130397\pi$
$601$			11736.6i			0.796583i	−0.917259	+	0.398291i	$0.869603\pi$
$602$	2874.07			0.194582
$603$	18146.7	+	18146.7i	1.22552	+	1.22552i
$604$	4058.81	−	4058.81i	0.273428	−	0.273428i
$605$	5398.25	−	7243.30i	0.362760	−	0.486747i
$606$	−15753.2	+	15753.2i	−1.05599	+	1.05599i
$607$		−	18800.6i		−	1.25715i	−0.777747	−	0.628577i	$-0.783638\pi$
$607$		−	18800.6i		−	1.25715i	0.777747	−	0.628577i	$-0.216362\pi$
$608$		−	12128.6i		−	0.809013i
$609$	7.60031	−	7.60031i	0.000505714	−	0.000505714i
$610$			7242.87i			0.480746i
$611$	8098.77	+	7660.57i	0.536237	+	0.507224i
$612$		−	37778.7i		−	2.49528i
$613$	1158.98	−	1158.98i	0.0763634	−	0.0763634i	−0.667893	−	0.744257i	$-0.732804\pi$
$613$	1158.98	−	1158.98i	0.0763634	−	0.0763634i	0.744257	+	0.667893i	$0.232804\pi$
$614$	29768.5			1.95661
$615$	14353.9			0.941146
$616$	−384.535	−	332.486i	−0.0251515	−	0.0217471i
$617$	3519.26	+	3519.26i	0.229628	+	0.229628i	0.812537	−	0.582909i	$-0.198086\pi$
$617$	3519.26	+	3519.26i	0.229628	+	0.229628i	−0.582909	+	0.812537i	$0.698086\pi$
$618$	38966.3	+	38966.3i	2.53633	+	2.53633i
$619$	−8574.63	+	8574.63i	−0.556774	+	0.556774i	−0.928388	−	0.371613i	$-0.878805\pi$
$619$	−8574.63	+	8574.63i	−0.556774	+	0.556774i	0.371613	+	0.928388i	$0.378805\pi$
$620$	−7065.10			−0.457647
$621$			4510.18i			0.291445i
$622$	−8211.80	−	8211.80i	−0.529362	−	0.529362i
$623$	2590.41			0.166585
$624$	512.566	+	18434.1i	0.0328831	+	1.18262i
$625$	−472.695			−0.0302525
$626$	24019.2	−	24019.2i	1.53354	−	1.53354i
$627$	−936.041	−	12894.7i	−0.0596202	−	0.821316i
$628$			22537.5i			1.43208i
$629$	−13982.2	+	13982.2i	−0.886337	+	0.886337i
$630$	−1566.02	−	1566.02i	−0.0990346	−	0.0990346i
$631$	15411.7	−	15411.7i	0.972312	−	0.972312i	−0.0273152	−	0.999627i	$-0.508696\pi$
$631$	15411.7	−	15411.7i	0.972312	−	0.972312i	0.999627	+	0.0273152i	$0.00869577\pi$
$632$	2499.19	−	2499.19i	0.157298	−	0.157298i
$633$		−	23403.1i		−	1.46950i
$634$	−10496.4			−0.657514
$635$	12862.0	+	12862.0i	0.803799	+	0.803799i
$636$		−	30249.6i		−	1.88596i
$637$	15757.7	−	438.150i	0.980133	−	0.0272530i
$638$	−83.0754	+	6.03052i	−0.00515515	+	0.000374217i
$639$	978.696	+	978.696i	0.0605894	+	0.0605894i
$640$			4620.53i			0.285379i
$641$			11265.5i			0.694169i	0.937834	+	0.347084i	$0.112828\pi$
$641$			11265.5i			0.694169i	−0.937834	+	0.347084i	$0.887172\pi$
$642$	10156.6	+	10156.6i	0.624373	+	0.624373i
$643$	−5779.87	−	5779.87i	−0.354488	−	0.354488i	0.507288	−	0.861776i	$-0.330648\pi$
$643$	−5779.87	−	5779.87i	−0.354488	−	0.354488i	−0.861776	+	0.507288i	$0.830648\pi$
$644$	3023.71	+	3023.71i	0.185017	+	0.185017i
$645$	−9714.39	−	9714.39i	−0.593029	−	0.593029i
$646$		−	26062.3i		−	1.58732i
$647$		−	2691.06i		−	0.163519i	−0.996652	−	0.0817594i	$-0.973946\pi$
$647$		−	2691.06i		−	0.163519i	0.996652	−	0.0817594i	$-0.0260539\pi$
$648$	−2390.96	−	2390.96i	−0.144947	−	0.144947i
$649$	162.861	+	2243.54i	0.00985032	+	0.135696i
$650$	−10573.7	+	11178.6i	−0.638055	+	0.674552i
$651$		−	2192.49i		−	0.131997i
$652$	−15860.4	−	15860.4i	−0.952673	−	0.952673i
$653$	−8587.09			−0.514608			−0.257304	−	0.966331i	$-0.582834\pi$
$653$	−8587.09			−0.514608			−0.257304	+	0.966331i	$0.582834\pi$
$654$		−	48791.6i		−	2.91728i
$655$	1606.04	−	1606.04i	0.0958062	−	0.0958062i
$656$	10259.6	−	10259.6i	0.610625	−	0.610625i
$657$	−10492.6	−	10492.6i	−0.623067	−	0.623067i
$658$	−1808.29	+	1808.29i	−0.107134	+	0.107134i
$659$		−	30049.1i		−	1.77625i	−0.459605	−	0.888124i	$-0.652009\pi$
$659$		−	30049.1i		−	1.77625i	0.459605	−	0.888124i	$-0.347991\pi$
$660$	1262.01	+	17385.2i	0.0744296	+	1.02533i
$661$	−4749.71	+	4749.71i	−0.279489	+	0.279489i	−0.832905	−	0.553416i	$-0.813324\pi$
$661$	−4749.71	+	4749.71i	−0.279489	+	0.279489i	0.553416	+	0.832905i	$0.313324\pi$
$662$	21733.7			1.27599
$663$	1321.20	+	47515.9i	0.0773923	+	2.78336i
$664$	1551.32			0.0906667
$665$	−580.647	−	580.647i	−0.0338594	−	0.0338594i
$666$		−	18635.8i		−	1.08427i
$667$	97.6746			0.00567013
$668$	2036.45	−	2036.45i	0.117953	−	0.117953i
$669$	−6805.60	−	6805.60i	−0.393303	−	0.393303i
$670$	−16878.4	−	16878.4i	−0.973239	−	0.973239i
$671$	7081.45	+	6122.93i	0.407416	+	0.352270i
$672$	−5074.54			−0.291301
$673$	−2897.31			−0.165948			−0.0829741	−	0.996552i	$-0.526442\pi$
$673$	−2897.31			−0.165948			−0.0829741	+	0.996552i	$0.526442\pi$
$674$	−19890.0	+	19890.0i	−1.13670	+	1.13670i
$675$		−	2000.95i		−	0.114099i
$676$	1134.86	+	20391.5i	0.0645689	+	1.16019i
$677$			19358.7i			1.09899i	0.835497	+	0.549495i	$0.185180\pi$
$677$			19358.7i			1.09899i	−0.835497	+	0.549495i	$0.814820\pi$
$678$	18022.8	−	18022.8i	1.02089	−	1.02089i
$679$			1049.88i			0.0593385i
$680$			4898.37i			0.276241i
$681$	−18983.2	+	18983.2i	−1.06819	+	1.06819i
$682$	−11112.7	+	12852.3i	−0.623940	+	0.721616i
$683$	23022.8	−	23022.8i	1.28981	−	1.28981i	0.354915	−	0.934898i	$-0.384510\pi$
$683$	23022.8	−	23022.8i	1.28981	−	1.28981i	0.934898	−	0.354915i	$-0.115490\pi$
$684$	9334.77	+	9334.77i	0.521819	+	0.521819i
$685$	7333.80			0.409066
$686$			7304.30i			0.406530i
$687$	18954.5	−	18954.5i	1.05264	−	1.05264i
$688$	−13886.9			−0.769527
$689$	559.820	+	20133.5i	0.0309542	+	1.11324i
$690$		−	38031.3i		−	2.09830i
$691$	−23860.5	−	23860.5i	−1.31360	−	1.31360i	−0.918745	−	0.394852i	$-0.870796\pi$
$691$	−23860.5	−	23860.5i	−1.31360	−	1.31360i	−0.394852	−	0.918745i	$-0.629204\pi$
$692$		−	13839.3i		−	0.760249i
$693$	−2854.99	+	207.247i	−0.156497	+	0.0113603i
$694$	−4952.48	−	4952.48i	−0.270884	−	0.270884i
$695$	−11212.8	+	11212.8i	−0.611981	+	0.611981i
$696$	15.8427	−	15.8427i	0.000862808	−	0.000862808i
$697$	26445.3	−	26445.3i	1.43714	−	1.43714i
$698$	7487.28			0.406014
$699$	30867.9			1.67029
$700$	−1341.47	−	1341.47i	−0.0724328	−	0.0724328i
$701$	27455.3			1.47927			0.739637	−	0.673006i	$-0.234997\pi$
$701$	27455.3			1.47927			0.739637	+	0.673006i	$0.234997\pi$
$702$	−3589.88	−	3395.64i	−0.193007	−	0.182564i
$703$		−	6909.74i		−	0.370705i
$704$	18276.6	+	15802.8i	0.978447	+	0.846008i
$705$	12224.1			0.653030
$706$	21383.4			1.13991
$707$	1293.24	+	1293.24i	0.0687937	+	0.0687937i
$708$	−3069.15	−	3069.15i	−0.162918	−	0.162918i
$709$	−24110.0	+	24110.0i	−1.27711	+	1.27711i	−0.334828	+	0.942279i	$0.608678\pi$
$709$	−24110.0	+	24110.0i	−1.27711	+	1.27711i	−0.942279	+	0.334828i	$0.891322\pi$
$710$	−910.294	−	910.294i	−0.0481165	−	0.0481165i
$711$		−	19902.3i		−	1.04978i
$712$	5399.64			0.284213
$713$	14088.3	−	14088.3i	0.739986	−	0.739986i
$714$	−10904.3			−0.571547
$715$	−1161.71	−	11547.9i	−0.0607629	−	0.604008i
$716$	13513.5			0.705341
$717$	−17585.0	+	17585.0i	−0.915934	+	0.915934i
$718$	−34749.5			−1.80618
$719$			13131.3i			0.681105i	0.940226	+	0.340552i	$0.110614\pi$
$719$			13131.3i			0.681105i	−0.940226	+	0.340552i	$0.889386\pi$
$720$	7566.72	+	7566.72i	0.391660	+	0.391660i
$721$	3198.87	−	3198.87i	0.165232	−	0.165232i
$722$	−13730.7	−	13730.7i	−0.707764	−	0.707764i
$723$	−22879.7	−	22879.7i	−1.17691	−	1.17691i
$724$	26409.8			1.35568
$725$	−43.3336			−0.00221982
$726$	33610.9	+	25049.4i	1.71821	+	1.28054i
$727$		−	20260.7i		−	1.03360i	−0.856106	−	0.516800i	$-0.827123\pi$
$727$		−	20260.7i		−	1.03360i	0.856106	−	0.516800i	$-0.172877\pi$
$728$	−652.854	+	18.1529i	−0.0332368	+	0.000924161i
$729$	−24223.5			−1.23068
$730$	9759.25	+	9759.25i	0.494803	+	0.494803i
$731$	−35795.2			−1.81112
$732$	−18063.5			−0.912086
$733$	2586.14	−	2586.14i	0.130315	−	0.130315i	−0.638941	−	0.769256i	$-0.720627\pi$
$733$	2586.14	−	2586.14i	0.130315	−	0.130315i	0.769256	+	0.638941i	$0.220627\pi$
$734$	−9164.09	+	9164.09i	−0.460835	+	0.460835i
$735$	12222.9	−	12222.9i	0.613397	−	0.613397i
$736$	−32607.5	−	32607.5i	−1.63305	−	1.63305i
$737$	−30770.8	+	2233.68i	−1.53793	+	0.111640i
$738$			35246.9i			1.75807i
$739$	11424.8	+	11424.8i	0.568700	+	0.568700i	0.931764	−	0.363064i	$-0.118269\pi$
$739$	11424.8	+	11424.8i	0.568700	+	0.568700i	−0.363064	+	0.931764i	$0.618269\pi$
$740$			9315.99i			0.462787i
$741$	−12067.2	−	11414.3i	−0.598246	−	0.565877i
$742$	−4620.40			−0.228598
$743$	22540.7	−	22540.7i	1.11297	−	1.11297i	0.120226	−	0.992747i	$-0.461638\pi$
$743$	22540.7	−	22540.7i	1.11297	−	1.11297i	0.992747	−	0.120226i	$-0.0383618\pi$
$744$		−	4570.19i		−	0.225203i
$745$	−5403.36			−0.265723
$746$	−11278.8	−	11278.8i	−0.553549	−	0.553549i
$747$	6176.95	−	6176.95i	0.302547	−	0.302547i
$748$	34355.2	+	29705.0i	1.67934	+	1.45203i
$749$	833.786	−	833.786i	0.0406754	−	0.0406754i
$750$			43591.8i			2.12233i
$751$			11207.1i			0.544546i	0.962220	+	0.272273i	$0.0877753\pi$
$751$			11207.1i			0.544546i	−0.962220	+	0.272273i	$0.912225\pi$
$752$	8737.31	−	8737.31i	0.423693	−	0.423693i
$753$			23281.0i			1.12670i
$754$	−73.5377	+	77.7441i	−0.00355184	+	0.00375501i
$755$			4190.90i			0.202017i
$756$	430.801	−	430.801i	0.0207250	−	0.0207250i
$757$	−5891.76			−0.282879			−0.141440	−	0.989947i	$-0.545173\pi$
$757$	−5891.76			−0.282879			−0.141440	+	0.989947i	$0.545173\pi$
$758$	−44492.9			−2.13200
$759$	−37183.7	−	32150.6i	−1.77824	−	1.53754i
$760$	−1210.34	−	1210.34i	−0.0577682	−	0.0577682i
$761$	−27634.4	−	27634.4i	−1.31636	−	1.31636i	−0.916637	−	0.399720i	$-0.869107\pi$
$761$	−27634.4	−	27634.4i	−1.31636	−	1.31636i	−0.399720	−	0.916637i	$-0.630893\pi$
$762$	−59683.2	+	59683.2i	−2.83739	+	2.83739i
$763$	−4005.47			−0.190049
$764$			25921.8i			1.22751i
$765$	19504.1	+	19504.1i	0.921793	+	0.921793i
$766$	6306.55			0.297474
$767$	2099.57	+	1985.97i	0.0988409	+	0.0934930i
$768$	18680.9			0.877719
$769$	−8603.02	+	8603.02i	−0.403424	+	0.403424i	−0.879438	−	0.476014i	$-0.842081\pi$
$769$	−8603.02	+	8603.02i	−0.403424	+	0.403424i	0.476014	+	0.879438i	$0.342081\pi$
$770$	2655.46	−	192.762i	0.124280	−	0.00902165i
$771$			26472.9i			1.23657i
$772$	−17727.5	+	17727.5i	−0.826459	+	0.826459i
$773$	9636.48	+	9636.48i	0.448383	+	0.448383i	0.894817	−	0.446434i	$-0.147306\pi$
$773$	9636.48	+	9636.48i	0.448383	+	0.448383i	−0.446434	+	0.894817i	$0.647306\pi$
$774$	23854.3	−	23854.3i	1.10779	−	1.10779i
$775$	−6250.30	+	6250.30i	−0.289700	+	0.289700i
$776$			2188.46i			0.101238i
$777$	−2891.00			−0.133480
$778$	−21056.8	−	21056.8i	−0.970337	−	0.970337i
$779$			13068.8i			0.601076i
$780$	16269.5	+	15389.2i	0.746848	+	0.706439i
$781$	−1659.55	+	120.468i	−0.0760348	+	0.00551945i
$782$	−70068.0	−	70068.0i	−3.20413	−	3.20413i
$783$		−	13.9161i		−	0.000635150i
$784$		−	17472.9i		−	0.795957i
$785$	−11635.5	−	11635.5i	−0.529030	−	0.529030i
$786$	7452.46	+	7452.46i	0.338194	+	0.338194i
$787$	6736.90	+	6736.90i	0.305139	+	0.305139i	0.843021	−	0.537881i	$-0.180775\pi$
$787$	6736.90	+	6736.90i	0.305139	+	0.305139i	−0.537881	+	0.843021i	$0.680775\pi$
$788$	−23243.6	−	23243.6i	−1.05079	−	1.05079i
$789$			43756.8i			1.97438i
$790$			18511.3i			0.833674i
$791$	−1479.55	−	1479.55i	−0.0665066	−	0.0665066i
$792$	−5951.17	+	432.001i	−0.267002	+	0.0193819i
$793$	12022.7	−	334.296i	0.538385	−	0.0149700i
$794$		−	3302.00i		−	0.147586i
$795$	15617.0	+	15617.0i	0.696702	+	0.696702i
$796$	−5856.17			−0.260762
$797$		−	34203.7i		−	1.52015i	−0.649838	−	0.760073i	$-0.725163\pi$
$797$		−	34203.7i		−	1.52015i	0.649838	−	0.760073i	$-0.274837\pi$
$798$	2694.36	−	2694.36i	0.119523	−	0.119523i
$799$	22521.4	−	22521.4i	0.997185	−	0.997185i
$800$	14466.4	+	14466.4i	0.639330	+	0.639330i
$801$	21500.0	−	21500.0i	0.948396	−	0.948396i
$802$		−	7074.61i		−	0.311488i
$803$	17792.0	−	1291.54i	0.781899	−	0.0567588i
$804$	42094.3	−	42094.3i	1.84646	−	1.84646i
$805$	−3122.11			−0.136696
$806$	606.725	+	21820.4i	0.0265148	+	0.953587i
$807$	1395.80			0.0608855
$808$	2695.72	+	2695.72i	0.117370	+	0.117370i
$809$		−	15083.9i		−	0.655526i	−0.944760	−	0.327763i	$-0.893705\pi$
$809$		−	15083.9i		−	0.655526i	0.944760	−	0.327763i	$-0.106295\pi$
$810$	17709.7			0.768215
$811$	−24266.4	+	24266.4i	−1.05069	+	1.05069i	−0.0520451	+	0.998645i	$0.516574\pi$
$811$	−24266.4	+	24266.4i	−1.05069	+	1.05069i	−0.998645	+	0.0520451i	$0.983426\pi$
$812$	−9.32963	−	9.32963i	−0.000403209	−	0.000403209i
$813$	23476.0	+	23476.0i	1.01272	+	1.01272i
$814$	16947.0	+	14653.1i	0.729720	+	0.630948i
$815$	16376.6			0.703862
$816$	52687.7			2.26034
$817$	8844.67	−	8844.67i	0.378746	−	0.378746i
$818$			50902.3i			2.17574i
$819$	−2527.22	+	2671.78i	−0.107824	+	0.113992i
$820$		−	17619.9i		−	0.750381i
$821$	−12694.8	+	12694.8i	−0.539649	+	0.539649i	−0.923426	−	0.383777i	$-0.874623\pi$
$821$	−12694.8	+	12694.8i	−0.539649	+	0.539649i	0.383777	+	0.923426i	$0.374623\pi$
$822$			34030.9i			1.44399i
$823$			24322.5i			1.03017i	0.857139	+	0.515085i	$0.172240\pi$
$823$			24322.5i			1.03017i	−0.857139	+	0.515085i	$0.827760\pi$
$824$	6667.96	−	6667.96i	0.281905	−	0.281905i
$825$	16496.6	+	14263.7i	0.696168	+	0.601937i
$826$	−468.791	+	468.791i	−0.0197473	+	0.0197473i
$827$	−5565.20	−	5565.20i	−0.234003	−	0.234003i	0.580358	−	0.814361i	$-0.302913\pi$
$827$	−5565.20	−	5565.20i	−0.234003	−	0.234003i	−0.814361	+	0.580358i	$0.802913\pi$
$828$	50192.7			2.10666
$829$		−	11789.4i		−	0.493922i	−0.969025	−	0.246961i	$-0.920568\pi$
$829$		−	11789.4i		−	0.493922i	0.969025	−	0.246961i	$-0.0794319\pi$
$830$	−5745.23	+	5745.23i	−0.240265	+	0.240265i
$831$	−11491.7			−0.479714
$832$	31029.6	−	862.790i	1.29298	−	0.0359518i
$833$		−	45038.3i		−	1.87333i
$834$	−52030.6	−	52030.6i	−2.16028	−	2.16028i
$835$			2102.73i			0.0871472i
$836$	−15828.7	+	1149.02i	−0.654841	+	0.0475355i
$837$	−2007.22	−	2007.22i	−0.0828908	−	0.0828908i
$838$	33895.7	−	33895.7i	1.39726	−	1.39726i
$839$	−19675.4	+	19675.4i	−0.809619	+	0.809619i	−0.984576	−	0.174957i	$-0.944021\pi$
$839$	−19675.4	+	19675.4i	−0.809619	+	0.809619i	0.174957	+	0.984576i	$0.444021\pi$
$840$	−506.401	+	506.401i	−0.0208006	+	0.0208006i
$841$	24388.7			0.999988
$842$	28578.5			1.16969
$843$	−37823.6	−	37823.6i	−1.54533	−	1.54533i
$844$	−28728.1			−1.17164
$845$	−11113.5	−	9941.66i	−0.452443	−	0.404738i
$846$			30017.1i			1.21987i
$847$	2056.39	−	2759.23i	0.0834218	−	0.111934i
$848$	22324.9			0.904056
$849$	−69682.8			−2.81685
$850$	31085.8	+	31085.8i	1.25439	+	1.25439i
$851$	−18576.7	−	18576.7i	−0.748297	−	0.748297i
$852$	2270.25	−	2270.25i	0.0912881	−	0.0912881i
$853$	−7388.81	−	7388.81i	−0.296586	−	0.296586i	0.543089	−	0.839675i	$-0.317255\pi$
$853$	−7388.81	−	7388.81i	−0.296586	−	0.296586i	−0.839675	+	0.543089i	$0.817255\pi$
$854$			2759.07i			0.110554i
$855$	−9638.58			−0.385535
$856$	1738.01	−	1738.01i	0.0693970	−	0.0693970i
$857$	−14856.1			−0.592153			−0.296077	−	0.955164i	$-0.595678\pi$
$857$	−14856.1			−0.592153			−0.296077	+	0.955164i	$0.595678\pi$
$858$	53585.3	−	5390.65i	2.13213	−	0.214492i
$859$	−99.3195			−0.00394498			−0.00197249	−	0.999998i	$-0.500628\pi$
$859$	−99.3195			−0.00394498			−0.00197249	+	0.999998i	$0.500628\pi$
$860$	−11924.7	+	11924.7i	−0.472826	+	0.472826i
$861$	5467.91			0.216430
$862$		−	32708.6i		−	1.29241i
$863$	−22812.6	−	22812.6i	−0.899826	−	0.899826i	0.0955942	−	0.995420i	$-0.469525\pi$
$863$	−22812.6	−	22812.6i	−0.899826	−	0.899826i	−0.995420	+	0.0955942i	$0.969525\pi$
$864$	−4645.73	+	4645.73i	−0.182929	+	0.182929i
$865$	7144.87	+	7144.87i	0.280847	+	0.280847i
$866$	35043.9	+	35043.9i	1.37510	+	1.37510i
$867$	98603.3			3.86245
$868$	−2691.35			−0.105242
$869$	18098.8	+	15649.0i	0.706511	+	0.610880i
$870$			117.345i			0.00457285i
$871$	−27238.1	+	28796.1i	−1.05962	+	1.12023i
$872$	−8349.30			−0.324247
$873$	8713.89	+	8713.89i	0.337824	+	0.337824i
$874$	34626.4			1.34011
$875$	3578.59			0.138261
$876$	−24339.3	+	24339.3i	−0.938754	+	0.938754i
$877$	20859.7	−	20859.7i	0.803172	−	0.803172i	−0.180418	−	0.983590i	$-0.557745\pi$
$877$	20859.7	−	20859.7i	0.803172	−	0.803172i	0.983590	+	0.180418i	$0.0577450\pi$
$878$	−41444.2	+	41444.2i	−1.59302	+	1.59302i
$879$	−46518.4	−	46518.4i	−1.78501	−	1.78501i
$880$	−12830.7	+	931.390i	−0.491501	+	0.0356786i
$881$			14495.0i			0.554312i	0.960825	+	0.277156i	$0.0893919\pi$
$881$			14495.0i			0.554312i	−0.960825	+	0.277156i	$0.910608\pi$
$882$	30014.1	+	30014.1i	1.14583	+	1.14583i
$883$		−	49318.2i		−	1.87960i	−0.341723	−	0.939801i	$-0.611010\pi$
$883$		−	49318.2i		−	1.87960i	0.341723	−	0.939801i	$-0.388990\pi$
$884$	58327.4	−	1621.81i	2.21919	−	0.0617053i
$885$	3169.04			0.120368
$886$	−24114.5	+	24114.5i	−0.914383	+	0.914383i
$887$		−	19966.5i		−	0.755816i	−0.925843	−	0.377908i	$-0.876644\pi$
$887$		−	19966.5i		−	0.755816i	0.925843	−	0.377908i	$-0.123356\pi$
$888$	−6026.21			−0.227733
$889$	4899.59	+	4899.59i	0.184845	+	0.184845i
$890$	−19997.3	+	19997.3i	−0.753160	+	0.753160i
$891$	14971.3	−	17315.0i	0.562914	−	0.651036i
$892$	−8354.10	+	8354.10i	−0.313583	+	0.313583i
$893$			11129.7i			0.417067i
$894$		−	25073.1i		−	0.937997i
$895$	−6976.66	+	6976.66i	−0.260563	+	0.260563i
$896$			1760.12i			0.0656268i
$897$	−63129.5	+	1755.34i	−2.34987	+	0.0653391i
$898$		−	10255.4i		−	0.381101i
$899$	−43.4693	+	43.4693i	−0.00161266	+	0.00161266i
$900$	−22268.1			−0.824744
$901$	57544.9			2.12775
$902$	−32052.9	−	27714.3i	−1.18320	−	1.02304i
$903$	−3700.56	−	3700.56i	−0.136375	−	0.136375i
$904$	−3084.08	−	3084.08i	−0.113468	−	0.113468i
$905$	−13634.7	+	13634.7i	−0.500808	+	0.500808i
$906$	−19447.0			−0.713115
$907$			21281.5i			0.779098i	0.921006	+	0.389549i	$0.127369\pi$
$907$			21281.5i			0.779098i	−0.921006	+	0.389549i	$0.872631\pi$
$908$	23302.4	+	23302.4i	0.851673	+	0.851673i
$909$	21467.4			0.783308
$910$	2350.59	−	2485.05i	0.0856278	−	0.0905258i
$911$	−32819.6			−1.19359			−0.596797	−	0.802393i	$-0.703560\pi$
$911$	−32819.6			−1.19359			−0.596797	+	0.802393i	$0.703560\pi$
$912$	−13018.7	+	13018.7i	−0.472687	+	0.472687i
$913$	760.323	+	10474.1i	0.0275608	+	0.379672i
$914$			78355.7i			2.83564i
$915$	9325.70	−	9325.70i	0.336938	−	0.336938i
$916$	−23267.3	−	23267.3i	−0.839272	−	0.839272i
$917$	611.797	−	611.797i	0.0220320	−	0.0220320i
$918$	−9982.90	+	9982.90i	−0.358916	+	0.358916i
$919$			30517.0i			1.09539i	0.836679	+	0.547694i	$0.184494\pi$
$919$			30517.0i			1.09539i	−0.836679	+	0.547694i	$0.815506\pi$
$920$	−6507.97			−0.233219
$921$	−38329.0	−	38329.0i	−1.37132	−	1.37132i
$922$			26823.6i			0.958123i
$923$	−1469.02	+	1553.05i	−0.0523871	+	0.0553837i
$924$	480.744	+	6622.63i	0.0171161	+	0.235789i
$925$	8241.59	+	8241.59i	0.292953	+	0.292953i
$926$		−	38481.7i		−	1.36564i
$927$		−	53100.3i		−	1.88138i
$928$	100.610	+	100.610i	0.00355893	+	0.00355893i
$929$	−37425.2	−	37425.2i	−1.32172	−	1.32172i	−0.912380	−	0.409344i	$-0.865758\pi$
$929$	−37425.2	−	37425.2i	−1.32172	−	1.32172i	−0.409344	−	0.912380i	$-0.634242\pi$
$930$	16925.5	+	16925.5i	0.596784	+	0.596784i
$931$	11128.6	+	11128.6i	0.391755	+	0.391755i
$932$		−	37891.4i		−	1.33173i
$933$			21146.5i			0.742022i
$934$	−3860.12	−	3860.12i	−0.135232	−	0.135232i
$935$	−33072.5	+	2400.77i	−1.15678	+	0.0839716i
$936$	−5267.93	+	5569.26i	−0.183961	+	0.194484i
$937$			25477.0i			0.888259i	0.895963	+	0.444129i	$0.146487\pi$
$937$			25477.0i			0.888259i	−0.895963	+	0.444129i	$0.853513\pi$
$938$	−6429.59	−	6429.59i	−0.223810	−	0.223810i
$939$	−61852.7			−2.14961
$940$		−	15005.5i		−	0.520665i
$941$	8142.70	−	8142.70i	0.282087	−	0.282087i	−0.551854	−	0.833941i	$-0.686079\pi$
$941$	8142.70	−	8142.70i	0.282087	−	0.282087i	0.833941	+	0.551854i	$0.186079\pi$
$942$	53991.9	−	53991.9i	1.86747	−	1.86747i
$943$	35135.2	+	35135.2i	1.21332	+	1.21332i
$944$	2265.11	−	2265.11i	0.0780963	−	0.0780963i
$945$			444.821i			0.0153122i
$946$	2936.24	+	40449.1i	0.100915	+	1.39018i
$947$	−3849.74	+	3849.74i	−0.132101	+	0.132101i	−0.770066	−	0.637965i	$-0.779777\pi$
$947$	−3849.74	+	3849.74i	−0.132101	+	0.132101i	0.637965	+	0.770066i	$0.279777\pi$
$948$	−46166.7			−1.58167
$949$	15749.3	−	16650.2i	0.538719	−	0.569534i
$950$	−15362.1			−0.524643
$951$	13514.8	+	13514.8i	0.460828	+	0.460828i
$952$			1865.97i			0.0635255i
$953$	−12189.4			−0.414328			−0.207164	−	0.978306i	$-0.566423\pi$
$953$	−12189.4			−0.414328			−0.207164	+	0.978306i	$0.566423\pi$
$954$	−38348.6	+	38348.6i	−1.30145	+	1.30145i
$955$	−13382.7	−	13382.7i	−0.453460	−	0.453460i
$956$	21586.2	+	21586.2i	0.730279	+	0.730279i
$957$	114.730	+	99.2006i	0.00387533	+	0.00335078i
$958$	−38281.4			−1.29104
$959$	2793.71			0.0940704
$960$	24068.8	−	24068.8i	0.809186	−	0.809186i
$961$		−	17251.3i		−	0.579076i
$962$	28772.2	−	800.023i	0.964297	−	0.0268126i
$963$		−	13840.6i		−	0.463144i
$964$	−28085.6	+	28085.6i	−0.938358	+	0.938358i
$965$		−	18304.4i		−	0.610612i
$966$		−	14487.5i		−	0.482533i
$967$	3000.63	−	3000.63i	0.0997867	−	0.0997867i	−0.655451	−	0.755238i	$-0.727521\pi$
$967$	3000.63	−	3000.63i	0.0997867	−	0.0997867i	0.755238	+	0.655451i	$0.227521\pi$
$968$	4286.49	−	5751.55i	0.142327	−	0.190973i
$969$	−33557.1	+	33557.1i	−1.11250	+	1.11250i
$970$	−8104.86	−	8104.86i	−0.268280	−	0.268280i
$971$	18393.6			0.607907			0.303954	−	0.952687i	$-0.401693\pi$
$971$	18393.6			0.607907			0.303954	+	0.952687i	$0.401693\pi$
$972$			50529.8i			1.66743i
$973$	−4271.37	+	4271.37i	−0.140734	+	0.140734i
$974$	15527.1			0.510801
$975$	28007.6	−	778.761i	0.919959	−	0.0255798i
$976$		−	13331.3i		−	0.437218i
$977$	23162.7	+	23162.7i	0.758486	+	0.758486i	0.976047	−	0.217560i	$-0.0698099\pi$
$977$	23162.7	+	23162.7i	0.758486	+	0.758486i	−0.217560	+	0.976047i	$0.569810\pi$
$978$			75992.0i			2.48462i
$979$	2646.44	+	36456.9i	0.0863950	+	1.19016i
$980$	−15004.0	−	15004.0i	−0.489065	−	0.489065i
$981$	−33244.8	+	33244.8i	−1.08198	+	1.08198i
$982$	45939.6	−	45939.6i	1.49286	−	1.49286i
$983$	−15371.1	+	15371.1i	−0.498740	+	0.498740i	−0.911046	−	0.412305i	$-0.864724\pi$
$983$	−15371.1	+	15371.1i	−0.498740	+	0.498740i	0.412305	+	0.911046i	$0.364724\pi$
$984$	11397.7			0.369254
$985$	24000.1			0.776352
$986$	216.194	+	216.194i	0.00698279	+	0.00698279i
$987$	4656.60			0.150173
$988$	−14011.4	+	14812.9i	−0.451177	+	0.476985i
$989$		−	47557.4i		−	1.52906i
$990$	20440.0	−	23639.8i	0.656188	−	0.758911i
$991$	57471.3			1.84222			0.921109	−	0.389306i	$-0.127285\pi$
$991$	57471.3			1.84222			0.921109	+	0.389306i	$0.127285\pi$
$992$	29023.4			0.928925
$993$	−27983.7	−	27983.7i	−0.894296	−	0.894296i
$994$	−346.764	−	346.764i	−0.0110651	−	0.0110651i
$995$	3023.38	−	3023.38i	0.0963292	−	0.0963292i
$996$	−14328.5	−	14328.5i	−0.455838	−	0.455838i
$997$			24116.7i			0.766082i	0.923731	+	0.383041i	$0.125123\pi$
$997$			24116.7i			0.766082i	−0.923731	+	0.383041i	$0.874877\pi$
$998$	−29757.6			−0.943850
$999$	−2646.70	+	2646.70i	−0.0838218	+	0.0838218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.6	✓	80
11.10	odd	2	inner	143.4.g.a.21.35	yes	80
13.5	odd	4	inner	143.4.g.a.109.35	yes	80
143.109	even	4	inner	143.4.g.a.109.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.6	✓	80	1.1	even	1	trivial
143.4.g.a.21.35	yes	80	11.10	odd	2	inner
143.4.g.a.109.6	yes	80	143.109	even	4	inner
143.4.g.a.109.35	yes	80	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.94074 + 2.94074i) q^{2} +7.57281 q^{3} -9.29587i q^{4} +(4.79920 + 4.79920i) q^{5} +(-22.2696 + 22.2696i) q^{6} +(1.82819 + 1.82819i) q^{7} +(3.81081 + 3.81081i) q^{8} +30.3474 q^{9} +O(q^{10})\)	\(q+(-2.94074 + 2.94074i) q^{2} +7.57281 q^{3} -9.29587i q^{4} +(4.79920 + 4.79920i) q^{5} +(-22.2696 + 22.2696i) q^{6} +(1.82819 + 1.82819i) q^{7} +(3.81081 + 3.81081i) q^{8} +30.3474 q^{9} -28.2264 q^{10} +(-23.8618 + 27.5973i) q^{11} -70.3958i q^{12} +(1.30280 + 46.8541i) q^{13} -10.7524 q^{14} +(36.3434 + 36.3434i) q^{15} +51.9538 q^{16} +133.917 q^{17} +(-89.2437 + 89.2437i) q^{18} +(-33.0896 + 33.0896i) q^{19} +(44.6128 - 44.6128i) q^{20} +(13.8445 + 13.8445i) q^{21} +(-10.9850 - 151.328i) q^{22} +177.922i q^{23} +(28.8586 + 28.8586i) q^{24} -78.9353i q^{25} +(-141.617 - 133.954i) q^{26} +25.3493 q^{27} +(16.9946 - 16.9946i) q^{28} -0.548976i q^{29} -213.753 q^{30} +(-79.1825 - 79.1825i) q^{31} +(-183.269 + 183.269i) q^{32} +(-180.701 + 208.989i) q^{33} +(-393.814 + 393.814i) q^{34} +17.5477i q^{35} -282.106i q^{36} +(-104.409 + 104.409i) q^{37} -194.616i q^{38} +(9.86582 + 354.817i) q^{39} +36.5777i q^{40} +(197.476 - 197.476i) q^{41} -81.4262 q^{42} -267.294 q^{43} +(256.541 + 221.817i) q^{44} +(145.643 + 145.643i) q^{45} +(-523.220 - 523.220i) q^{46} +(168.175 - 168.175i) q^{47} +393.436 q^{48} -336.315i q^{49} +(232.128 + 232.128i) q^{50} +1014.13 q^{51} +(435.549 - 12.1106i) q^{52} +429.707 q^{53} +(-74.5455 + 74.5455i) q^{54} +(-246.963 + 17.9273i) q^{55} +13.9338i q^{56} +(-250.582 + 250.582i) q^{57} +(1.61439 + 1.61439i) q^{58} +(43.5985 - 43.5985i) q^{59} +(337.844 - 337.844i) q^{60} -256.599i q^{61} +465.710 q^{62} +(55.4808 + 55.4808i) q^{63} -662.261i q^{64} +(-218.610 + 231.115i) q^{65} +(-83.1876 - 1145.98i) q^{66} +(597.966 + 597.966i) q^{67} -1244.87i q^{68} +1347.37i q^{69} +(-51.6032 - 51.6032i) q^{70} +(32.2498 + 32.2498i) q^{71} +(115.648 + 115.648i) q^{72} +(-345.749 - 345.749i) q^{73} -614.082i q^{74} -597.762i q^{75} +(307.597 + 307.597i) q^{76} +(-94.0771 + 6.82915i) q^{77} +(-1072.44 - 1014.41i) q^{78} -655.816i q^{79} +(249.337 + 249.337i) q^{80} -627.415 q^{81} +1161.45i q^{82} +(203.541 - 203.541i) q^{83} +(128.697 - 128.697i) q^{84} +(642.694 + 642.694i) q^{85} +(786.042 - 786.042i) q^{86} -4.15729i q^{87} +(-196.101 + 14.2352i) q^{88} +(708.463 - 708.463i) q^{89} -856.598 q^{90} +(-83.2763 + 88.0398i) q^{91} +1653.94 q^{92} +(-599.634 - 599.634i) q^{93} +989.116i q^{94} -317.608 q^{95} +(-1387.86 + 1387.86i) q^{96} +(287.138 + 287.138i) q^{97} +(989.015 + 989.015i) q^{98} +(-724.145 + 837.507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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