LMFDB - Embedded newform 143.4.g.a.21.15

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			21.15
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47926 + 1.47926i) q^{2} +4.19980 q^{3} +3.62357i q^{4} +(-3.33873 - 3.33873i) q^{5} +(-6.21261 + 6.21261i) q^{6} +(-14.0682 - 14.0682i) q^{7} +(-17.1943 - 17.1943i) q^{8} -9.36165 q^{9} +O(q^{10})$	\(q+(-1.47926 + 1.47926i) q^{2} +4.19980 q^{3} +3.62357i q^{4} +(-3.33873 - 3.33873i) q^{5} +(-6.21261 + 6.21261i) q^{6} +(-14.0682 - 14.0682i) q^{7} +(-17.1943 - 17.1943i) q^{8} -9.36165 q^{9} +9.87770 q^{10} +(6.16113 - 35.9589i) q^{11} +15.2183i q^{12} +(-46.3749 + 6.80934i) q^{13} +41.6210 q^{14} +(-14.0220 - 14.0220i) q^{15} +21.8812 q^{16} +26.5068 q^{17} +(13.8483 - 13.8483i) q^{18} +(-12.3429 + 12.3429i) q^{19} +(12.0981 - 12.0981i) q^{20} +(-59.0836 - 59.0836i) q^{21} +(44.0786 + 62.3065i) q^{22} +107.013i q^{23} +(-72.2127 - 72.2127i) q^{24} -102.706i q^{25} +(58.5278 - 78.6734i) q^{26} -152.712 q^{27} +(50.9770 - 50.9770i) q^{28} -1.95546i q^{29} +41.4844 q^{30} +(-135.464 - 135.464i) q^{31} +(105.186 - 105.186i) q^{32} +(25.8756 - 151.020i) q^{33} +(-39.2105 + 39.2105i) q^{34} +93.9396i q^{35} -33.9226i q^{36} +(171.012 - 171.012i) q^{37} -36.5167i q^{38} +(-194.766 + 28.5979i) q^{39} +114.814i q^{40} +(-124.780 + 124.780i) q^{41} +174.800 q^{42} +138.040 q^{43} +(130.300 + 22.3253i) q^{44} +(31.2560 + 31.2560i) q^{45} +(-158.301 - 158.301i) q^{46} +(-149.651 + 149.651i) q^{47} +91.8965 q^{48} +52.8270i q^{49} +(151.929 + 151.929i) q^{50} +111.323 q^{51} +(-24.6741 - 168.043i) q^{52} -303.294 q^{53} +(225.901 - 225.901i) q^{54} +(-140.627 + 99.4865i) q^{55} +483.785i q^{56} +(-51.8377 + 51.8377i) q^{57} +(2.89264 + 2.89264i) q^{58} +(-463.740 + 463.740i) q^{59} +(50.8097 - 50.8097i) q^{60} +345.071i q^{61} +400.773 q^{62} +(131.701 + 131.701i) q^{63} +486.246i q^{64} +(177.568 + 132.099i) q^{65} +(185.122 + 261.675i) q^{66} +(-126.329 - 126.329i) q^{67} +96.0493i q^{68} +449.435i q^{69} +(-138.961 - 138.961i) q^{70} +(156.692 + 156.692i) q^{71} +(160.967 + 160.967i) q^{72} +(437.006 + 437.006i) q^{73} +505.944i q^{74} -431.344i q^{75} +(-44.7254 - 44.7254i) q^{76} +(-592.552 + 419.200i) q^{77} +(245.805 - 330.413i) q^{78} +63.8018i q^{79} +(-73.0552 - 73.0552i) q^{80} -388.595 q^{81} -369.164i q^{82} +(579.595 - 579.595i) q^{83} +(214.094 - 214.094i) q^{84} +(-88.4990 - 88.4990i) q^{85} +(-204.198 + 204.198i) q^{86} -8.21256i q^{87} +(-724.224 + 512.351i) q^{88} +(495.749 - 495.749i) q^{89} -92.4716 q^{90} +(748.205 + 556.615i) q^{91} -387.771 q^{92} +(-568.922 - 568.922i) q^{93} -442.746i q^{94} +82.4191 q^{95} +(441.762 - 441.762i) q^{96} +(-952.162 - 952.162i) q^{97} +(-78.1449 - 78.1449i) q^{98} +(-57.6784 + 336.635i) 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 $

$2$	−1.47926	+	1.47926i	−0.522998	+	0.522998i	−0.918476	−	0.395478i	$-0.870579\pi$
$2$	−1.47926	+	1.47926i	−0.522998	+	0.522998i	0.395478	+	0.918476i	$0.370579\pi$
$3$	4.19980			0.808252			0.404126	−	0.914703i	$-0.367576\pi$
$3$	4.19980			0.808252			0.404126	+	0.914703i	$0.367576\pi$
$4$			3.62357i			0.452946i
$5$	−3.33873	−	3.33873i	−0.298625	−	0.298625i	0.541850	−	0.840475i	$-0.317724\pi$
$5$	−3.33873	−	3.33873i	−0.298625	−	0.298625i	−0.840475	+	0.541850i	$0.817724\pi$
$6$	−6.21261	+	6.21261i	−0.422714	+	0.422714i
$7$	−14.0682	−	14.0682i	−0.759610	−	0.759610i	0.216641	−	0.976251i	$-0.430490\pi$
$7$	−14.0682	−	14.0682i	−0.759610	−	0.759610i	−0.976251	+	0.216641i	$0.930490\pi$
$8$	−17.1943	−	17.1943i	−0.759888	−	0.759888i
$9$	−9.36165			−0.346728
$10$	9.87770			0.312360
$11$	6.16113	−	35.9589i	0.168877	−	0.985637i
$11$	6.16113	−	35.9589i	0.168877	−	0.985637i
$12$			15.2183i			0.366095i
$13$	−46.3749	+	6.80934i	−0.989391	+	0.145275i
$13$	−46.3749	+	6.80934i	−0.989391	+	0.145275i
$14$	41.6210			0.794549
$15$	−14.0220	−	14.0220i	−0.241364	−	0.241364i
$16$	21.8812			0.341893
$17$	26.5068			0.378167			0.189084	−	0.981961i	$-0.439448\pi$
$17$	26.5068			0.378167			0.189084	+	0.981961i	$0.439448\pi$
$18$	13.8483	−	13.8483i	0.181338	−	0.181338i
$19$	−12.3429	+	12.3429i	−0.149034	+	0.149034i	−0.777687	−	0.628652i	$-0.783607\pi$
$19$	−12.3429	+	12.3429i	−0.149034	+	0.149034i	0.628652	+	0.777687i	$0.283607\pi$
$20$	12.0981	−	12.0981i	0.135261	−	0.135261i
$21$	−59.0836	−	59.0836i	−0.613957	−	0.613957i
$22$	44.0786	+	62.3065i	0.427164	+	0.603809i
$23$			107.013i			0.970167i	0.874468	+	0.485083i	$0.161211\pi$
$23$			107.013i			0.970167i	−0.874468	+	0.485083i	$0.838789\pi$
$24$	−72.2127	−	72.2127i	−0.614181	−	0.614181i
$25$		−	102.706i		−	0.821646i
$26$	58.5278	−	78.6734i	0.441471	−	0.593428i
$27$	−152.712			−1.08850
$28$	50.9770	−	50.9770i	0.344063	−	0.344063i
$29$		−	1.95546i		−	0.0125214i	−0.999980	−	0.00626070i	$-0.998007\pi$
$29$		−	1.95546i		−	0.0125214i	0.999980	−	0.00626070i	$-0.00199285\pi$
$30$	41.4844			0.252466
$31$	−135.464	−	135.464i	−0.784840	−	0.784840i	0.195803	−	0.980643i	$-0.437269\pi$
$31$	−135.464	−	135.464i	−0.784840	−	0.784840i	−0.980643	+	0.195803i	$0.937269\pi$
$32$	105.186	−	105.186i	0.581079	−	0.581079i
$33$	25.8756	−	151.020i	0.136496	−	0.796644i
$34$	−39.2105	+	39.2105i	−0.197781	+	0.197781i
$35$			93.9396i			0.453677i
$36$		−	33.9226i		−	0.157049i
$37$	171.012	−	171.012i	0.759845	−	0.759845i	−0.216449	−	0.976294i	$-0.569447\pi$
$37$	171.012	−	171.012i	0.759845	−	0.759845i	0.976294	+	0.216449i	$0.0694474\pi$
$38$		−	36.5167i		−	0.155889i
$39$	−194.766	+	28.5979i	−0.799678	+	0.117419i
$40$			114.814i			0.453843i
$41$	−124.780	+	124.780i	−0.475301	+	0.475301i	−0.903625	−	0.428324i	$-0.859104\pi$
$41$	−124.780	+	124.780i	−0.475301	+	0.475301i	0.428324	+	0.903625i	$0.359104\pi$
$42$	174.800			0.642196
$43$	138.040			0.489557			0.244779	−	0.969579i	$-0.421285\pi$
$43$	138.040			0.489557			0.244779	+	0.969579i	$0.421285\pi$
$44$	130.300	+	22.3253i	0.446441	+	0.0764924i
$45$	31.2560	+	31.2560i	0.103542	+	0.103542i
$46$	−158.301	−	158.301i	−0.507395	−	0.507395i
$47$	−149.651	+	149.651i	−0.464444	+	0.464444i	−0.900109	−	0.435665i	$-0.856513\pi$
$47$	−149.651	+	149.651i	−0.464444	+	0.464444i	0.435665	+	0.900109i	$0.356513\pi$
$48$	91.8965			0.276336
$49$			52.8270i			0.154015i
$50$	151.929	+	151.929i	0.429719	+	0.429719i
$51$	111.323			0.305655
$52$	−24.6741	−	168.043i	−0.0658017	−	0.448141i
$53$	−303.294			−0.786049			−0.393025	−	0.919528i	$-0.628571\pi$
$53$	−303.294			−0.786049			−0.393025	+	0.919528i	$0.628571\pi$
$54$	225.901	−	225.901i	0.569281	−	0.569281i
$55$	−140.627	+	99.4865i	−0.344767	+	0.243905i
$56$			483.785i			1.15444i
$57$	−51.8377	+	51.8377i	−0.120457	+	0.120457i
$58$	2.89264	+	2.89264i	0.00654866	+	0.00654866i
$59$	−463.740	+	463.740i	−1.02328	+	1.02328i	−0.0235624	+	0.999722i	$0.507501\pi$
$59$	−463.740	+	463.740i	−1.02328	+	1.02328i	−0.999722	+	0.0235624i	$0.992499\pi$
$60$	50.8097	−	50.8097i	0.109325	−	0.109325i
$61$			345.071i			0.724293i	0.932121	+	0.362146i	$0.117956\pi$
$61$			345.071i			0.724293i	−0.932121	+	0.362146i	$0.882044\pi$
$62$	400.773			0.820940
$63$	131.701	+	131.701i	0.263378	+	0.263378i
$64$			486.246i			0.949699i
$65$	177.568	+	132.099i	0.338839	+	0.252074i
$66$	185.122	+	261.675i	0.345256	+	0.488030i
$67$	−126.329	−	126.329i	−0.230351	−	0.230351i	0.582488	−	0.812839i	$-0.302079\pi$
$67$	−126.329	−	126.329i	−0.230351	−	0.230351i	−0.812839	+	0.582488i	$0.802079\pi$
$68$			96.0493i			0.171290i
$69$			449.435i			0.784140i
$70$	−138.961	−	138.961i	−0.237272	−	0.237272i
$71$	156.692	+	156.692i	0.261915	+	0.261915i	0.825832	−	0.563917i	$-0.190706\pi$
$71$	156.692	+	156.692i	0.261915	+	0.261915i	−0.563917	+	0.825832i	$0.690706\pi$
$72$	160.967	+	160.967i	0.263474	+	0.263474i
$73$	437.006	+	437.006i	0.700653	+	0.700653i	0.964551	−	0.263898i	$-0.0850082\pi$
$73$	437.006	+	437.006i	0.700653	+	0.700653i	−0.263898	+	0.964551i	$0.585008\pi$
$74$			505.944i			0.794795i
$75$		−	431.344i		−	0.664098i
$76$	−44.7254	−	44.7254i	−0.0675046	−	0.0675046i
$77$	−592.552	+	419.200i	−0.876981	+	0.620419i
$78$	245.805	−	330.413i	0.356820	−	0.479640i
$79$			63.8018i			0.0908641i	0.998967	+	0.0454321i	$0.0144665\pi$
$79$			63.8018i			0.0908641i	−0.998967	+	0.0454321i	$0.985534\pi$
$80$	−73.0552	−	73.0552i	−0.102098	−	0.102098i
$81$	−388.595			−0.533052
$82$		−	369.164i		−	0.497163i
$83$	579.595	−	579.595i	0.766492	−	0.766492i	−0.210995	−	0.977487i	$-0.567670\pi$
$83$	579.595	−	579.595i	0.766492	−	0.766492i	0.977487	+	0.210995i	$0.0676703\pi$
$84$	214.094	−	214.094i	0.278089	−	0.278089i
$85$	−88.4990	−	88.4990i	−0.112930	−	0.112930i
$86$	−204.198	+	204.198i	−0.256037	+	0.256037i
$87$		−	8.21256i		−	0.0101204i
$88$	−724.224	+	512.351i	−0.877302	+	0.620646i
$89$	495.749	−	495.749i	0.590442	−	0.590442i	−0.347309	−	0.937751i	$-0.612904\pi$
$89$	495.749	−	495.749i	0.590442	−	0.590442i	0.937751	+	0.347309i	$0.112904\pi$
$90$	−92.4716			−0.108304
$91$	748.205	+	556.615i	0.861904	+	0.641199i
$92$	−387.771			−0.439434
$93$	−568.922	−	568.922i	−0.634349	−	0.634349i
$94$		−	442.746i		−	0.485806i
$95$	82.4191			0.0890107
$96$	441.762	−	441.762i	0.469658	−	0.469658i
$97$	−952.162	−	952.162i	−0.996675	−	0.996675i	0.00331991	−	0.999994i	$-0.498943\pi$
$97$	−952.162	−	952.162i	−0.996675	−	0.996675i	−0.999994	+	0.00331991i	$0.998943\pi$
$98$	−78.1449	−	78.1449i	−0.0805493	−	0.0805493i
$99$	−57.6784	+	336.635i	−0.0585545	+	0.341748i
$100$	372.162			0.372162
$101$	−1815.06			−1.78817			−0.894083	−	0.447901i	$-0.852172\pi$
$101$	−1815.06			−1.78817			−0.894083	+	0.447901i	$0.852172\pi$
$102$	−164.676	+	164.676i	−0.159857	+	0.159857i
$103$		−	1025.73i		−	0.981248i	−0.871371	−	0.490624i	$-0.836769\pi$
$103$		−	1025.73i		−	0.981248i	0.871371	−	0.490624i	$-0.163231\pi$
$104$	914.466	+	680.302i	0.862219	+	0.641434i
$105$			394.528i			0.366685i
$106$	448.651	−	448.651i	0.411102	−	0.411102i
$107$			200.397i			0.181057i	0.995894	+	0.0905284i	$0.0288556\pi$
$107$			200.397i			0.181057i	−0.995894	+	0.0905284i	$0.971144\pi$
$108$		−	553.362i		−	0.493031i
$109$	993.759	−	993.759i	0.873256	−	0.873256i	−0.119570	−	0.992826i	$-0.538152\pi$
$109$	993.759	−	993.759i	0.873256	−	0.873256i	0.992826	+	0.119570i	$0.0381516\pi$
$110$	60.8578	−	355.191i	0.0527506	−	0.307874i
$111$	718.219	−	718.219i	0.614147	−	0.614147i
$112$	−307.828	−	307.828i	−0.259705	−	0.259705i
$113$	2189.88			1.82307			0.911536	−	0.411221i	$-0.134898\pi$
$113$	2189.88			1.82307			0.911536	+	0.411221i	$0.134898\pi$
$114$		−	153.363i		−	0.125998i
$115$	357.288	−	357.288i	0.289716	−	0.289716i
$116$	7.08576			0.00567152
$117$	434.146	−	63.7467i	0.343050	−	0.0503708i
$118$		−	1371.99i		−	1.07035i
$119$	−372.902	−	372.902i	−0.287260	−	0.287260i
$120$			482.197i			0.366820i
$121$	−1255.08	−	443.095i	−0.942961	−	0.332904i
$122$	−510.451	−	510.451i	−0.378803	−	0.378803i
$123$	−524.051	+	524.051i	−0.384163	+	0.384163i
$124$	490.863	−	490.863i	0.355491	−	0.355491i
$125$	−760.247	+	760.247i	−0.543989	+	0.543989i
$126$	−389.642			−0.275492
$127$	−2050.93			−1.43300			−0.716498	−	0.697590i	$-0.754256\pi$
$127$	−2050.93			−1.43300			−0.716498	+	0.697590i	$0.754256\pi$
$128$	122.207	+	122.207i	0.0843882	+	0.0843882i
$129$	579.742			0.395686
$130$	−458.077	+	67.2606i	−0.309047	+	0.0453781i
$131$			1300.27i			0.867215i	0.901102	+	0.433607i	$0.142760\pi$
$131$			1300.27i			0.867215i	−0.901102	+	0.433607i	$0.857240\pi$
$132$	547.232	+	93.7619i	0.360837	+	0.0618252i
$133$	347.284			0.226416
$134$	373.747			0.240946
$135$	509.863	+	509.863i	0.325052	+	0.325052i
$136$	−455.766	−	455.766i	−0.287365	−	0.287365i
$137$	−767.088	+	767.088i	−0.478371	+	0.478371i	−0.904610	−	0.426240i	$-0.859838\pi$
$137$	−767.088	+	767.088i	−0.478371	+	0.478371i	0.426240	+	0.904610i	$0.359838\pi$
$138$	−664.832	−	664.832i	−0.410103	−	0.410103i
$139$		−	1553.08i		−	0.947703i	−0.880605	−	0.473851i	$-0.842863\pi$
$139$		−	1553.08i		−	0.947703i	0.880605	−	0.473851i	$-0.157137\pi$
$140$	−340.397			−0.205491
$141$	−628.505	+	628.505i	−0.375388	+	0.375388i
$142$	−463.577			−0.273962
$143$	−40.8658	+	1709.54i	−0.0238977	+	0.999714i
$144$	−204.844			−0.118544
$145$	−6.52876	+	6.52876i	−0.00373920	+	0.00373920i
$146$	−1292.89			−0.732880
$147$			221.863i			0.124483i
$148$	619.676	+	619.676i	0.344169	+	0.344169i
$149$	−1244.98	+	1244.98i	−0.684514	+	0.684514i	−0.961014	−	0.276500i	$-0.910825\pi$
$149$	−1244.98	+	1244.98i	−0.684514	+	0.684514i	0.276500	+	0.961014i	$0.410825\pi$
$150$	638.071	+	638.071i	0.347322	+	0.347322i
$151$	472.304	+	472.304i	0.254540	+	0.254540i	0.822829	−	0.568289i	$-0.192394\pi$
$151$	472.304	+	472.304i	0.254540	+	0.254540i	−0.568289	+	0.822829i	$0.692394\pi$
$152$	424.455			0.226499
$153$	−248.148			−0.131121
$154$	256.433	−	1496.64i	0.134181	−	0.783137i
$155$			904.554i			0.468746i
$156$	−103.627	−	705.747i	−0.0531844	−	0.362211i
$157$	317.320			0.161305			0.0806525	−	0.996742i	$-0.474300\pi$
$157$	317.320			0.161305			0.0806525	+	0.996742i	$0.474300\pi$
$158$	−94.3796	−	94.3796i	−0.0475217	−	0.0475217i
$159$	−1273.77			−0.635326
$160$	−702.378			−0.347049
$161$	1505.48	−	1505.48i	0.736948	−	0.736948i
$162$	574.833	−	574.833i	0.278785	−	0.278785i
$163$	2194.02	−	2194.02i	1.05429	−	1.05429i	0.0558477	−	0.998439i	$-0.482214\pi$
$163$	2194.02	−	2194.02i	1.05429	−	1.05429i	0.998439	−	0.0558477i	$-0.0177861\pi$
$164$	−452.149	−	452.149i	−0.215286	−	0.215286i
$165$	−590.606	+	417.824i	−0.278658	+	0.197137i
$166$			1714.75i			0.801748i
$167$	−559.822	−	559.822i	−0.259403	−	0.259403i	0.565408	−	0.824811i	$-0.308719\pi$
$167$	−559.822	−	559.822i	−0.259403	−	0.259403i	−0.824811	+	0.565408i	$0.808719\pi$
$168$			2031.80i			0.933076i
$169$	2104.27	−	631.565i	0.957790	−	0.287467i
$170$	261.826			0.118124
$171$	115.550	−	115.550i	0.0516744	−	0.0516744i
$172$			500.199i			0.221743i
$173$	4013.18			1.76368			0.881839	−	0.471551i	$-0.156306\pi$
$173$	4013.18			1.76368			0.881839	+	0.471551i	$0.156306\pi$
$174$	12.1485	+	12.1485i	0.00529297	+	0.00529297i
$175$	−1444.88	+	1444.88i	−0.624131	+	0.624131i
$176$	134.813	−	786.822i	0.0577380	−	0.336982i
$177$	−1947.62	+	1947.62i	−0.827072	+	0.827072i
$178$			1466.69i			0.617600i
$179$		−	732.581i		−	0.305898i	−0.988234	−	0.152949i	$-0.951123\pi$
$179$		−	732.581i		−	0.305898i	0.988234	−	0.152949i	$-0.0488770\pi$
$180$	−113.258	+	113.258i	−0.0468988	+	0.0468988i
$181$		−	2221.29i		−	0.912194i	−0.889930	−	0.456097i	$-0.849247\pi$
$181$		−	2221.29i		−	0.912194i	0.889930	−	0.456097i	$-0.150753\pi$
$182$	−1930.17	+	283.412i	−0.786120	+	0.115428i
$183$			1449.23i			0.585411i
$184$	1840.02	−	1840.02i	0.737218	−	0.737218i
$185$	−1141.93			−0.453817
$186$	1683.17			0.663526
$187$	163.312	−	953.155i	0.0638639	−	0.372736i
$188$	−542.271	−	542.271i	−0.210368	−	0.210368i
$189$	2148.38	+	2148.38i	0.826833	+	0.826833i
$190$	−121.919	+	121.919i	−0.0465524	+	0.0465524i
$191$	−2211.12			−0.837649			−0.418825	−	0.908067i	$-0.637558\pi$
$191$	−2211.12			−0.837649			−0.418825	+	0.908067i	$0.637558\pi$
$192$			2042.14i			0.767596i
$193$	−2768.03	−	2768.03i	−1.03237	−	1.03237i	−0.999458	−	0.0329097i	$-0.989523\pi$
$193$	−2768.03	−	2768.03i	−1.03237	−	1.03237i	−0.0329097	−	0.999458i	$-0.510477\pi$
$194$	2816.99			1.04252
$195$	745.749	+	554.788i	0.273868	+	0.203740i
$196$	−191.422			−0.0697603
$197$	331.173	−	331.173i	0.119772	−	0.119772i	−0.644680	−	0.764452i	$-0.723009\pi$
$197$	331.173	−	331.173i	0.119772	−	0.119772i	0.764452	+	0.644680i	$0.223009\pi$
$198$	−412.649	−	583.292i	−0.148110	−	0.209357i
$199$			2552.35i			0.909204i	0.890695	+	0.454602i	$0.150219\pi$
$199$			2552.35i			0.909204i	−0.890695	+	0.454602i	$0.849781\pi$
$200$	−1765.95	+	1765.95i	−0.624359	+	0.624359i
$201$	−530.556	−	530.556i	−0.186182	−	0.186182i
$202$	2684.94	−	2684.94i	0.935207	−	0.935207i
$203$	−27.5098	+	27.5098i	−0.00951137	+	0.00951137i
$204$			403.388i			0.138445i
$205$	833.212			0.283873
$206$	1517.33	+	1517.33i	0.513191	+	0.513191i
$207$		−	1001.82i		−	0.336384i
$208$	−1014.74	+	148.996i	−0.338266	+	0.0496684i
$209$	367.790	+	519.883i	0.121725	+	0.172062i
$210$	−583.610	−	583.610i	−0.191776	−	0.191776i
$211$		−	4429.22i		−	1.44512i	−0.691308	−	0.722560i	$-0.742965\pi$
$211$		−	4429.22i		−	1.44512i	0.691308	−	0.722560i	$-0.257035\pi$
$212$		−	1099.01i		−	0.356038i
$213$	658.076	+	658.076i	0.211693	+	0.211693i
$214$	−296.439	−	296.439i	−0.0946923	−	0.0946923i
$215$	−460.879	−	460.879i	−0.146194	−	0.146194i
$216$	2625.77	+	2625.77i	0.827135	+	0.827135i
$217$			3811.46i			1.19234i
$218$			2940.06i			0.913422i
$219$	1835.34	+	1835.34i	0.566304	+	0.566304i
$220$	−360.496	−	509.573i	−0.110476	−	0.156161i
$221$	−1229.25	+	180.494i	−0.374156	+	0.0549382i
$222$			2124.87i			0.642395i
$223$	−823.358	−	823.358i	−0.247247	−	0.247247i	0.572593	−	0.819840i	$-0.305938\pi$
$223$	−823.358	−	823.358i	−0.247247	−	0.247247i	−0.819840	+	0.572593i	$0.805938\pi$
$224$	−2959.56			−0.882786
$225$			961.496i			0.284888i
$226$	−3239.41	+	3239.41i	−0.953462	+	0.953462i
$227$	4403.18	−	4403.18i	1.28744	−	1.28744i	0.351108	−	0.936335i	$-0.385805\pi$
$227$	4403.18	−	4403.18i	1.28744	−	1.28744i	0.936335	−	0.351108i	$-0.114195\pi$
$228$	−187.838	−	187.838i	−0.0545608	−	0.0545608i
$229$	−2965.60	+	2965.60i	−0.855774	+	0.855774i	−0.990837	−	0.135063i	$-0.956876\pi$
$229$	−2965.60	+	2965.60i	−0.855774	+	0.855774i	0.135063	+	0.990837i	$0.456876\pi$
$230$			1057.05i			0.303042i
$231$	−2488.60	+	1760.56i	−0.708822	+	0.501455i
$232$	−33.6228	+	33.6228i	−0.00951486	+	0.00951486i
$233$	3456.03			0.971726			0.485863	−	0.874035i	$-0.338505\pi$
$233$	3456.03			0.971726			0.485863	+	0.874035i	$0.338505\pi$
$234$	−547.917	+	736.513i	−0.153070	+	0.205758i
$235$	999.288			0.277389
$236$	−1680.40	−	1680.40i	−0.463493	−	0.463493i
$237$			267.955i			0.0734411i
$238$	1103.24			0.300472
$239$	2101.72	−	2101.72i	0.568824	−	0.568824i	−0.362975	−	0.931799i	$-0.618239\pi$
$239$	2101.72	−	2101.72i	0.568824	−	0.568824i	0.931799	+	0.362975i	$0.118239\pi$
$240$	−306.817	−	306.817i	−0.0825207	−	0.0825207i
$241$	893.515	+	893.515i	0.238823	+	0.238823i	0.816363	−	0.577540i	$-0.195987\pi$
$241$	893.515	+	893.515i	0.238823	+	0.238823i	−0.577540	+	0.816363i	$0.695987\pi$
$242$	2512.05	−	1201.14i	0.667274	−	0.319059i
$243$	2491.20			0.657656
$244$	−1250.39			−0.328066
$245$	176.375	−	176.375i	0.0459926	−	0.0459926i
$246$		−	1550.42i		−	0.401833i
$247$	488.354	−	656.448i	0.125802	−	0.169104i
$248$			4658.42i			1.19278i
$249$	2434.19	−	2434.19i	0.619519	−	0.619519i
$250$		−	2249.21i		−	0.569010i
$251$			108.109i			0.0271864i	0.999908	+	0.0135932i	$0.00432699\pi$
$251$			108.109i			0.0271864i	−0.999908	+	0.0135932i	$0.995673\pi$
$252$	−477.229	+	477.229i	−0.119296	+	0.119296i
$253$	3848.08	+	659.324i	0.956232	+	0.163839i
$254$	3033.86	−	3033.86i	0.749453	−	0.749453i
$255$	−371.678	−	371.678i	−0.0912761	−	0.0912761i
$256$	−4251.52			−1.03797
$257$			6303.90i			1.53007i	0.643992	+	0.765033i	$0.277277\pi$
$257$			6303.90i			1.53007i	−0.643992	+	0.765033i	$0.722723\pi$
$258$	−857.591	+	857.591i	−0.206943	+	0.206943i
$259$	−4811.67			−1.15437
$260$	−478.669	+	643.429i	−0.114176	+	0.153476i
$261$			18.3064i			0.00434152i
$262$	−1923.44	−	1923.44i	−0.453551	−	0.453551i
$263$		−	3326.16i		−	0.779847i	−0.920847	−	0.389923i	$-0.872501\pi$
$263$		−	3326.16i		−	0.779847i	0.920847	−	0.389923i	$-0.127499\pi$
$264$	−3041.60	+	2151.77i	−0.709081	+	0.501638i
$265$	1012.62	+	1012.62i	0.234734	+	0.234734i
$266$	−513.724	+	513.724i	−0.118415	+	0.118415i
$267$	2082.05	−	2082.05i	0.477226	−	0.477226i
$268$	457.762	−	457.762i	0.104337	−	0.104337i
$269$	5602.32			1.26981			0.634906	−	0.772589i	$-0.281039\pi$
$269$	5602.32			1.26981			0.634906	+	0.772589i	$0.281039\pi$
$270$	−1508.44			−0.340003
$271$	−4036.75	−	4036.75i	−0.904853	−	0.904853i	0.0909984	−	0.995851i	$-0.470994\pi$
$271$	−4036.75	−	4036.75i	−0.904853	−	0.904853i	−0.995851	+	0.0909984i	$0.970994\pi$
$272$	580.000			0.129293
$273$	3142.32	+	2337.67i	0.696636	+	0.518251i
$274$		−	2269.45i		−	0.500374i
$275$	−3693.18	−	632.784i	−0.809845	−	0.138758i
$276$	−1628.56			−0.355173
$277$	−1958.49			−0.424816			−0.212408	−	0.977181i	$-0.568131\pi$
$277$	−1958.49			−0.424816			−0.212408	+	0.977181i	$0.568131\pi$
$278$	2297.41	+	2297.41i	0.495646	+	0.495646i
$279$	1268.17	+	1268.17i	0.272126	+	0.272126i
$280$	1615.23	−	1615.23i	0.344743	−	0.344743i
$281$	−4141.90	−	4141.90i	−0.879306	−	0.879306i	0.114157	−	0.993463i	$-0.463583\pi$
$281$	−4141.90	−	4141.90i	−0.879306	−	0.879306i	−0.993463	+	0.114157i	$0.963583\pi$
$282$		−	1859.45i		−	0.392654i
$283$	230.771			0.0484732			0.0242366	−	0.999706i	$-0.492284\pi$
$283$	230.771			0.0484732			0.0242366	+	0.999706i	$0.492284\pi$
$284$	−567.785	+	567.785i	−0.118633	+	0.118633i
$285$	346.144			0.0719432
$286$	−2468.41	−	2589.31i	−0.510350	−	0.535347i
$287$	3510.85			0.722087
$288$	−984.719	+	984.719i	−0.201476	+	0.201476i
$289$	−4210.39			−0.856989
$290$		−	19.3155i		−	0.00391119i
$291$	−3998.89	−	3998.89i	−0.805565	−	0.805565i
$292$	−1583.52	+	1583.52i	−0.317358	+	0.317358i
$293$	4784.83	+	4784.83i	0.954037	+	0.954037i	0.998989	−	0.0449522i	$-0.0143136\pi$
$293$	4784.83	+	4784.83i	0.954037	+	0.954037i	−0.0449522	+	0.998989i	$0.514314\pi$
$294$	−328.193	−	328.193i	−0.0651041	−	0.0651041i
$295$	3096.60			0.611156
$296$	−5880.88			−1.15479
$297$	−940.878	+	5491.34i	−0.183822	+	1.07286i
$298$		−	3683.29i		−	0.715998i
$299$	−728.691	−	4962.74i	−0.140941	−	0.959875i
$300$	1563.01			0.300801
$301$	−1941.98	−	1941.98i	−0.371873	−	0.371873i
$302$	−1397.32			−0.266248
$303$	−7622.88			−1.44529
$304$	−270.077	+	270.077i	−0.0509538	+	0.0509538i
$305$	1152.10	−	1152.10i	0.216292	−	0.216292i
$306$	367.075	−	367.075i	0.0685761	−	0.0685761i
$307$	−7109.43	−	7109.43i	−1.32168	−	1.32168i	−0.912413	−	0.409270i	$-0.865783\pi$
$307$	−7109.43	−	7109.43i	−1.32168	−	1.32168i	−0.409270	−	0.912413i	$-0.634217\pi$
$308$	−1519.00	−	2147.15i	−0.281016	−	0.397225i
$309$		−	4307.88i		−	0.793096i
$310$	−1338.07	−	1338.07i	−0.245153	−	0.245153i
$311$		−	7155.10i		−	1.30459i	−0.757964	−	0.652297i	$-0.773806\pi$
$311$		−	7155.10i		−	1.30459i	0.757964	−	0.652297i	$-0.226194\pi$
$312$	3840.58	+	2857.14i	0.696891	+	0.518441i
$313$	6250.88			1.12882			0.564410	−	0.825495i	$-0.309104\pi$
$313$	6250.88			1.12882			0.564410	+	0.825495i	$0.309104\pi$
$314$	−469.399	+	469.399i	−0.0843622	+	0.0843622i
$315$		−	879.430i		−	0.157302i
$316$	−231.190			−0.0411566
$317$	−145.374	−	145.374i	−0.0257571	−	0.0257571i	0.694111	−	0.719868i	$-0.255798\pi$
$317$	−145.374	−	145.374i	−0.0257571	−	0.0257571i	−0.719868	+	0.694111i	$0.755798\pi$
$318$	1884.25	−	1884.25i	0.332274	−	0.332274i
$319$	−70.3163	−	12.0479i	−0.0123415	−	0.00211458i
$320$	1623.44	−	1623.44i	0.283604	−	0.283604i
$321$			841.627i			0.146340i
$322$			4454.01i			0.770845i
$323$	−327.171	+	327.171i	−0.0563600	+	0.0563600i
$324$		−	1408.10i		−	0.241444i
$325$	699.359	+	4762.97i	0.119364	+	0.812930i
$326$			6491.05i			1.10278i
$327$	4173.59	−	4173.59i	0.705811	−	0.705811i
$328$	4291.01			0.722351
$329$	4210.63			0.705592
$330$	255.591	−	1491.73i	0.0426358	−	0.248840i
$331$	−3311.13	−	3311.13i	−0.549837	−	0.549837i	0.376556	−	0.926394i	$-0.377108\pi$
$331$	−3311.13	−	3311.13i	−0.549837	−	0.549837i	−0.926394	+	0.376556i	$0.877108\pi$
$332$	2100.21	+	2100.21i	0.347180	+	0.347180i
$333$	−1600.96	+	1600.96i	−0.263460	+	0.263460i
$334$	1656.25			0.271335
$335$			843.555i			0.137577i
$336$	−1292.82	−	1292.82i	−0.209907	−	0.209907i
$337$	10987.2			1.77600			0.887998	−	0.459847i	$-0.152096\pi$
$337$	10987.2			1.77600			0.887998	+	0.459847i	$0.152096\pi$
$338$	−2178.51	+	4047.01i	−0.350578	+	0.651267i
$339$	9197.09			1.47350
$340$	320.682	−	320.682i	0.0511513	−	0.0511513i
$341$	−5705.74	+	4036.52i	−0.906109	+	0.641026i
$342$			341.857i			0.0540512i
$343$	−4082.20	+	4082.20i	−0.642619	+	0.642619i
$344$	−2373.51	−	2373.51i	−0.372009	−	0.372009i
$345$	1500.54	−	1500.54i	0.234164	−	0.234164i
$346$	−5936.54	+	5936.54i	−0.922400	+	0.922400i
$347$		−	4769.14i		−	0.737813i	−0.929467	−	0.368906i	$-0.879732\pi$
$347$		−	4769.14i		−	0.737813i	0.929467	−	0.368906i	$-0.120268\pi$
$348$	29.7588			0.00458402
$349$	2036.39	+	2036.39i	0.312336	+	0.312336i	0.845814	−	0.533478i	$-0.179115\pi$
$349$	2036.39	+	2036.39i	0.312336	+	0.312336i	−0.533478	+	0.845814i	$0.679115\pi$
$350$		−	4274.72i		−	0.652838i
$351$	7082.00	−	1039.87i	1.07695	−	0.158131i
$352$	−3134.32	−	4430.45i	−0.474602	−	0.670864i
$353$	−6081.59	−	6081.59i	−0.916970	−	0.916970i	0.0798381	−	0.996808i	$-0.474560\pi$
$353$	−6081.59	−	6081.59i	−0.916970	−	0.916970i	−0.996808	+	0.0798381i	$0.974560\pi$
$354$		−	5762.07i		−	0.865114i
$355$		−	1046.30i		−	0.156428i
$356$	1796.38	+	1796.38i	0.267439	+	0.267439i
$357$	−1566.12	−	1566.12i	−0.232178	−	0.232178i
$358$	1083.68	+	1083.68i	0.159984	+	0.159984i
$359$	−2289.92	−	2289.92i	−0.336650	−	0.336650i	0.518455	−	0.855105i	$-0.326507\pi$
$359$	−2289.92	−	2289.92i	−0.336650	−	0.336650i	−0.855105	+	0.518455i	$0.826507\pi$
$360$		−	1074.85i		−	0.157360i
$361$			6554.31i			0.955577i
$362$	3285.87	+	3285.87i	0.477075	+	0.477075i
$363$	−5271.09	−	1860.91i	−0.762150	−	0.269070i
$364$	−2016.94	+	2711.18i	−0.290429	+	0.390396i
$365$		−	2918.08i		−	0.418464i
$366$	−2143.79	−	2143.79i	−0.306169	−	0.306169i
$367$	2344.54			0.333471			0.166736	−	0.986002i	$-0.446677\pi$
$367$	2344.54			0.333471			0.166736	+	0.986002i	$0.446677\pi$
$368$			2341.58i			0.331693i
$369$	1168.15	−	1168.15i	0.164800	−	0.164800i
$370$	1689.21	−	1689.21i	0.237345	−	0.237345i
$371$	4266.79	+	4266.79i	0.597091	+	0.597091i
$372$	2061.53	−	2061.53i	0.287326	−	0.287326i
$373$			8705.21i			1.20841i	0.796827	+	0.604207i	$0.206510\pi$
$373$			8705.21i			1.20841i	−0.796827	+	0.604207i	$0.793490\pi$
$374$	1168.38	+	1651.55i	0.161539	+	0.228341i
$375$	−3192.89	+	3192.89i	−0.439680	+	0.439680i
$376$	5146.29			0.705850
$377$	13.3154	+	90.6844i	0.00181904	+	0.0123886i
$378$	−6356.02			−0.864863
$379$	7881.13	+	7881.13i	1.06814	+	1.06814i	0.997502	+	0.0706418i	$0.0225047\pi$
$379$	7881.13	+	7881.13i	1.06814	+	1.06814i	0.0706418	+	0.997502i	$0.477495\pi$
$380$			298.651i			0.0403171i
$381$	−8613.49			−1.15822
$382$	3270.82	−	3270.82i	0.438089	−	0.438089i
$383$	1158.67	+	1158.67i	0.154583	+	0.154583i	0.780161	−	0.625578i	$-0.215137\pi$
$383$	1158.67	+	1158.67i	0.154583	+	0.154583i	−0.625578	+	0.780161i	$0.715137\pi$
$384$	513.246	+	513.246i	0.0682070	+	0.0682070i
$385$	3377.96	+	578.774i	0.447161	+	0.0766158i
$386$	8189.27			1.07985
$387$	−1292.29			−0.169743
$388$	3450.23	−	3450.23i	0.451440	−	0.451440i
$389$			1397.14i			0.182103i	0.995846	+	0.0910513i	$0.0290227\pi$
$389$			1397.14i			0.182103i	−0.995846	+	0.0910513i	$0.970977\pi$
$390$	−1923.84	+	282.481i	−0.249788	+	0.0366769i
$391$			2836.58i			0.366885i
$392$	908.323	−	908.323i	0.117034	−	0.117034i
$393$			5460.88i			0.700929i
$394$			979.782i			0.125281i
$395$	213.017	−	213.017i	0.0271343	−	0.0271343i
$396$	−1219.82	−	209.002i	−0.154794	−	0.0265221i
$397$	−7586.17	+	7586.17i	−0.959041	+	0.959041i	−0.999194	−	0.0401529i	$-0.987215\pi$
$397$	−7586.17	+	7586.17i	−0.959041	+	0.959041i	0.0401529	+	0.999194i	$0.487215\pi$
$398$	−3775.60	−	3775.60i	−0.475512	−	0.475512i
$399$	1458.52			0.183001
$400$		−	2247.32i		−	0.280915i
$401$	−4538.67	+	4538.67i	−0.565213	+	0.565213i	−0.930784	−	0.365571i	$-0.880874\pi$
$401$	−4538.67	+	4538.67i	−0.565213	+	0.565213i	0.365571	+	0.930784i	$0.380874\pi$
$402$	1569.66			0.194745
$403$	7204.55	+	5359.71i	0.890532	+	0.662497i
$404$		−	6576.98i		−	0.809944i
$405$	1297.41	+	1297.41i	0.159182	+	0.159182i
$406$		−	81.3884i		−	0.00994886i
$407$	−5095.78	−	7203.05i	−0.620611	−	0.877252i
$408$	−1914.13	−	1914.13i	−0.232263	−	0.232263i
$409$	−6902.69	+	6902.69i	−0.834513	+	0.834513i	−0.988130	−	0.153617i	$-0.950908\pi$
$409$	−6902.69	+	6902.69i	−0.834513	+	0.834513i	0.153617	+	0.988130i	$0.450908\pi$
$410$	−1232.54	+	1232.54i	−0.148465	+	0.148465i
$411$	−3221.62	+	3221.62i	−0.386644	+	0.386644i
$412$	3716.82			0.444453
$413$	13047.9			1.55459
$414$	1481.96	+	1481.96i	0.175928	+	0.175928i
$415$	−3870.22			−0.457787
$416$	−4161.76	+	5594.26i	−0.490498	+	0.659330i
$417$		−	6522.64i		−	0.765983i
$418$	−1313.10	−	224.984i	−0.153650	−	0.0263262i
$419$	−3928.81			−0.458079			−0.229039	−	0.973417i	$-0.573558\pi$
$419$	−3928.81			−0.458079			−0.229039	+	0.973417i	$0.573558\pi$
$420$	−1429.60			−0.166089
$421$	−2976.08	−	2976.08i	−0.344525	−	0.344525i	0.513540	−	0.858066i	$-0.328334\pi$
$421$	−2976.08	−	2976.08i	−0.344525	−	0.344525i	−0.858066	+	0.513540i	$0.828334\pi$
$422$	6551.98	+	6551.98i	0.755795	+	0.755795i
$423$	1400.98	−	1400.98i	0.161036	−	0.161036i
$424$	5214.93	+	5214.93i	0.597309	+	0.597309i
$425$		−	2722.40i		−	0.310720i
$426$	−1946.93			−0.221430
$427$	4854.52	−	4854.52i	0.550180	−	0.550180i
$428$	−726.152			−0.0820090
$429$	−171.628	+	7179.74i	−0.0193154	+	0.808022i
$430$	1363.52			0.152918
$431$	−8092.42	+	8092.42i	−0.904404	+	0.904404i	−0.995813	−	0.0914098i	$-0.970863\pi$
$431$	−8092.42	+	8092.42i	−0.904404	+	0.904404i	0.0914098	+	0.995813i	$0.470863\pi$
$432$	−3341.51			−0.372149
$433$		−	1347.11i		−	0.149510i	−0.997202	−	0.0747552i	$-0.976182\pi$
$433$		−	1347.11i		−	0.149510i	0.997202	−	0.0747552i	$-0.0238175\pi$
$434$	−5638.15	−	5638.15i	−0.623594	−	0.623594i
$435$	−27.4195	+	27.4195i	−0.00302222	+	0.00302222i
$436$	3600.96	+	3600.96i	0.395538	+	0.395538i
$437$	−1320.85	−	1320.85i	−0.144588	−	0.144588i
$438$	−5429.89			−0.592352
$439$	−2513.53			−0.273267			−0.136633	−	0.990622i	$-0.543628\pi$
$439$	−2513.53			−0.273267			−0.136633	+	0.990622i	$0.543628\pi$
$440$	4128.59	+	707.385i	0.447324	+	0.0766438i
$441$		−	494.548i		−	0.0534011i
$442$	1551.39	−	2085.38i	0.166950	−	0.224415i
$443$	5114.03			0.548476			0.274238	−	0.961662i	$-0.411574\pi$
$443$	5114.03			0.548476			0.274238	+	0.961662i	$0.411574\pi$
$444$	2602.52	+	2602.52i	0.278176	+	0.278176i
$445$	−3310.34			−0.352641
$446$	2435.92			0.258620
$447$	−5228.66	+	5228.66i	−0.553260	+	0.553260i
$448$	6840.59	−	6840.59i	0.721401	−	0.721401i
$449$	−3377.87	+	3377.87i	−0.355037	+	0.355037i	−0.861980	−	0.506943i	$-0.830776\pi$
$449$	−3377.87	+	3377.87i	−0.355037	+	0.355037i	0.506943	+	0.861980i	$0.330776\pi$
$450$	−1422.30	−	1422.30i	−0.148996	−	0.148996i
$451$	3718.16	+	5255.73i	0.388207	+	0.548742i
$452$			7935.21i			0.825754i
$453$	1983.59	+	1983.59i	0.205733	+	0.205733i
$454$			13026.9i			1.34666i
$455$	−639.667	−	4356.44i	−0.0659078	−	0.448864i
$456$	1782.63			0.183068
$457$	11486.9	−	11486.9i	1.17578	−	1.17578i	0.194973	−	0.980809i	$-0.437538\pi$
$457$	11486.9	−	11486.9i	1.17578	−	1.17578i	0.980809	−	0.194973i	$-0.0624620\pi$
$458$		−	8773.79i		−	0.895136i
$459$	−4047.90			−0.411634
$460$	1294.66	+	1294.66i	0.131226	+	0.131226i
$461$	−7217.91	+	7217.91i	−0.729222	+	0.729222i	−0.970465	−	0.241242i	$-0.922445\pi$
$461$	−7217.91	+	7217.91i	−0.729222	+	0.729222i	0.241242	+	0.970465i	$0.422445\pi$
$462$	1076.97	−	6285.61i	0.108452	−	0.632972i
$463$	−5942.57	+	5942.57i	−0.596489	+	0.596489i	−0.939377	−	0.342887i	$-0.888595\pi$
$463$	−5942.57	+	5942.57i	−0.596489	+	0.596489i	0.342887	+	0.939377i	$0.388595\pi$
$464$		−	42.7878i		−	0.00428098i
$465$			3798.95i			0.378865i
$466$	−5112.37	+	5112.37i	−0.508211	+	0.508211i
$467$			7259.72i			0.719357i	0.933076	+	0.359678i	$0.117114\pi$
$467$			7259.72i			0.719357i	−0.933076	+	0.359678i	$0.882886\pi$
$468$	230.991	+	1573.16i	0.0228153	+	0.155383i
$469$			3554.43i			0.349954i
$470$	−1478.21	+	1478.21i	−0.145074	+	0.145074i
$471$	1332.68			0.130375
$472$	15947.4			1.55516
$473$	850.485	−	4963.78i	0.0826752	−	0.482526i
$474$	−396.376	−	396.376i	−0.0384096	−	0.0384096i
$475$	1267.69	+	1267.69i	0.122454	+	0.122454i
$476$	1351.24	−	1351.24i	0.130113	−	0.130113i
$477$	2839.33			0.272545
$478$			6217.98i			0.594987i
$479$	−1038.47	−	1038.47i	−0.0990583	−	0.0990583i	0.655841	−	0.754899i	$-0.272314\pi$
$479$	−1038.47	−	1038.47i	−0.0990583	−	0.0990583i	−0.754899	+	0.655841i	$0.772314\pi$
$480$	−2949.85			−0.280503
$481$	−6766.21	+	9095.17i	−0.641398	+	0.862171i
$482$	−2643.48			−0.249808
$483$	6322.73	−	6322.73i	0.595640	−	0.595640i
$484$	1605.59	−	4547.88i	0.150788	−	0.427111i
$485$			6358.02i			0.595263i
$486$	−3685.13	+	3685.13i	−0.343953	+	0.343953i
$487$	−9063.73	−	9063.73i	−0.843361	−	0.843361i	0.145934	−	0.989294i	$-0.453381\pi$
$487$	−9063.73	−	9063.73i	−0.843361	−	0.843361i	−0.989294	+	0.145934i	$0.953381\pi$
$488$	5933.26	−	5933.26i	0.550381	−	0.550381i
$489$	9214.44	−	9214.44i	0.852130	−	0.852130i
$490$			521.809i			0.0481080i
$491$	−2987.37			−0.274579			−0.137289	−	0.990531i	$-0.543839\pi$
$491$	−2987.37			−0.274579			−0.137289	+	0.990531i	$0.543839\pi$
$492$	−1898.94	−	1898.94i	−0.174005	−	0.174005i
$493$		−	51.8331i		−	0.00473518i
$494$	248.655	+	1693.46i	0.0226468	+	0.154236i
$495$	1316.50	−	931.358i	0.119540	−	0.0845686i
$496$	−2964.11	−	2964.11i	−0.268331	−	0.268331i
$497$		−	4408.74i		−	0.397906i
$498$			7201.60i			0.648015i
$499$	−12154.9	−	12154.9i	−1.09044	−	1.09044i	−0.995481	−	0.0949566i	$-0.969729\pi$
$499$	−12154.9	−	12154.9i	−1.09044	−	1.09044i	−0.0949566	−	0.995481i	$-0.530271\pi$
$500$	−2754.81	−	2754.81i	−0.246398	−	0.246398i
$501$	−2351.14	−	2351.14i	−0.209663	−	0.209663i
$502$	−159.922	−	159.922i	−0.0142185	−	0.0142185i
$503$			8761.94i			0.776691i	0.921514	+	0.388345i	$0.126953\pi$
$503$			8761.94i			0.776691i	−0.921514	+	0.388345i	$0.873047\pi$
$504$		−	4529.03i		−	0.400276i
$505$	6059.97	+	6059.97i	0.533991	+	0.533991i
$506$	−6667.63	+	4717.00i	−0.585795	+	0.414420i
$507$	8837.50	−	2652.45i	0.774137	−	0.232346i
$508$		−	7431.68i		−	0.649070i
$509$	−6214.67	−	6214.67i	−0.541180	−	0.541180i	0.382695	−	0.923875i	$-0.374996\pi$
$509$	−6214.67	−	6214.67i	−0.541180	−	0.541180i	−0.923875	+	0.382695i	$0.874996\pi$
$510$	1099.62			0.0954744
$511$		−	12295.7i		−	1.06445i
$512$	5311.45	−	5311.45i	0.458467	−	0.458467i
$513$	1884.91	−	1884.91i	0.162223	−	0.162223i
$514$	−9325.12	−	9325.12i	−0.800221	−	0.800221i
$515$	−3424.65	+	3424.65i	−0.293025	+	0.293025i
$516$			2100.74i			0.179225i
$517$	4459.26	+	6303.30i	0.379339	+	0.536207i
$518$	7117.71	−	7117.71i	0.603734	−	0.603734i
$519$	16854.6			1.42550
$520$	−781.809	−	5324.50i	−0.0659319	−	0.449028i
$521$	7622.73			0.640994			0.320497	−	0.947250i	$-0.396150\pi$
$521$	7622.73			0.640994			0.320497	+	0.947250i	$0.396150\pi$
$522$	−27.0799	−	27.0799i	−0.00227060	−	0.00227060i
$523$		−	6584.03i		−	0.550477i	−0.961376	−	0.275239i	$-0.911243\pi$
$523$		−	6584.03i		−	0.550477i	0.961376	−	0.275239i	$-0.0887569\pi$
$524$	−4711.62			−0.392802
$525$	−6068.22	+	6068.22i	−0.504455	+	0.504455i
$526$	4920.26	+	4920.26i	0.407858	+	0.407858i
$527$	−3590.72	−	3590.72i	−0.296801	−	0.296801i
$528$	566.187	−	3304.50i	0.0466669	−	0.272367i
$529$	715.135			0.0587766
$530$	−2995.85			−0.245531
$531$	4341.37	−	4341.37i	0.354801	−	0.354801i
$532$			1258.41i			0.102554i
$533$	4936.99	−	6636.33i	0.401210	−	0.539308i
$534$			6159.79i			0.499176i
$535$	669.070	−	669.070i	0.0540681	−	0.0540681i
$536$			4344.27i			0.350082i
$537$		−	3076.70i		−	0.247243i
$538$	−8287.30	+	8287.30i	−0.664109	+	0.664109i
$539$	1899.60	+	325.474i	0.151802	+	0.0260096i
$540$	−1847.52	+	1847.52i	−0.147231	+	0.147231i
$541$	3914.49	+	3914.49i	0.311085	+	0.311085i	0.845330	−	0.534245i	$-0.179404\pi$
$541$	3914.49	+	3914.49i	0.311085	+	0.311085i	−0.534245	+	0.845330i	$0.679404\pi$
$542$	11942.8			0.946472
$543$		−	9328.97i		−	0.737283i
$544$	2788.16	−	2788.16i	0.219745	−	0.219745i
$545$	−6635.78			−0.521552
$546$	−8106.34	+	1190.27i	−0.635383	+	0.0932949i
$547$		−	18316.7i		−	1.43175i	−0.698229	−	0.715875i	$-0.746028\pi$
$547$		−	18316.7i		−	1.43175i	0.698229	−	0.715875i	$-0.253972\pi$
$548$	−2779.60	−	2779.60i	−0.216676	−	0.216676i
$549$		−	3230.44i		−	0.251132i
$550$	6399.24	−	4527.13i	0.496117	−	0.350977i
$551$	24.1361	+	24.1361i	0.00186612	+	0.00186612i
$552$	7727.72	−	7727.72i	0.595858	−	0.595858i
$553$	897.575	−	897.575i	0.0690213	−	0.0690213i
$554$	2897.11	−	2897.11i	0.222178	−	0.222178i
$555$	−4795.87			−0.366799
$556$	5627.70			0.429259
$557$	−15655.9	−	15655.9i	−1.19095	−	1.19095i	−0.976800	−	0.214152i	$-0.931301\pi$
$557$	−15655.9	−	15655.9i	−1.19095	−	1.19095i	−0.214152	−	0.976800i	$-0.568699\pi$
$558$	−3751.90			−0.284643
$559$	−6401.61	+	939.964i	−0.484364	+	0.0711203i
$560$			2055.51i			0.155109i
$561$	685.878	−	4003.06i	0.0516182	−	0.301265i
$562$	12253.9			0.919750
$563$	−7057.12			−0.528281			−0.264141	−	0.964484i	$-0.585088\pi$
$563$	−7057.12			−0.528281			−0.264141	+	0.964484i	$0.585088\pi$
$564$	−2277.43	−	2277.43i	−0.170031	−	0.170031i
$565$	−7311.43	−	7311.43i	−0.544414	−	0.544414i
$566$	−341.371	+	341.371i	−0.0253514	+	0.0253514i
$567$	5466.82	+	5466.82i	0.404911	+	0.404911i
$568$		−	5388.42i		−	0.398051i
$569$	−9132.23			−0.672835			−0.336418	−	0.941713i	$-0.609215\pi$
$569$	−9132.23			−0.672835			−0.336418	+	0.941713i	$0.609215\pi$
$570$	−512.037	+	512.037i	−0.0376261	+	0.0376261i
$571$	−19542.5			−1.43227			−0.716135	−	0.697961i	$-0.754091\pi$
$571$	−19542.5			−1.43227			−0.716135	+	0.697961i	$0.754091\pi$
$572$	−6194.65	−	148.080i	−0.452817	−	0.0108244i
$573$	−9286.27			−0.677032
$574$	−5193.47	+	5193.47i	−0.377650	+	0.377650i
$575$	10990.9			0.797134
$576$		−	4552.06i		−	0.329287i
$577$	−733.216	−	733.216i	−0.0529015	−	0.0529015i	0.680161	−	0.733063i	$-0.261910\pi$
$577$	−733.216	−	733.216i	−0.0529015	−	0.0529015i	−0.733063	+	0.680161i	$0.761910\pi$
$578$	6228.27	−	6228.27i	0.448204	−	0.448204i
$579$	−11625.2	−	11625.2i	−0.834414	−	0.834414i
$580$	−23.6574	−	23.6574i	−0.00169366	−	0.00169366i
$581$	−16307.7			−1.16447
$582$	11830.8			0.842617
$583$	−1868.63	+	10906.1i	−0.132746	+	0.774759i
$584$		−	15028.0i		−	1.06483i
$585$	−1662.33	−	1236.66i	−0.117485	−	0.0874012i
$586$	−14156.0			−0.997919
$587$	18503.7	+	18503.7i	1.30107	+	1.30107i	0.927668	+	0.373405i	$0.121810\pi$
$587$	18503.7	+	18503.7i	1.30107	+	1.30107i	0.373405	+	0.927668i	$0.378190\pi$
$588$	−803.936			−0.0563840
$589$	3344.03			0.233936
$590$	−4580.68	+	4580.68i	−0.319633	+	0.319633i
$591$	1390.86	−	1390.86i	0.0968060	−	0.0968060i
$592$	3741.95	−	3741.95i	0.259786	−	0.259786i
$593$	−10803.6	−	10803.6i	−0.748146	−	0.748146i	0.225985	−	0.974131i	$-0.427440\pi$
$593$	−10803.6	−	10803.6i	−0.748146	−	0.748146i	−0.974131	+	0.225985i	$0.927440\pi$
$594$	−6731.33	−	9514.94i	−0.464966	−	0.657243i
$595$			2490.04i			0.171566i
$596$	−4511.27	−	4511.27i	−0.310048	−	0.310048i
$597$			10719.4i			0.734866i
$598$	8419.11	+	6263.26i	0.575724	+	0.428301i
$599$	−8092.68			−0.552016			−0.276008	−	0.961155i	$-0.589012\pi$
$599$	−8092.68			−0.552016			−0.276008	+	0.961155i	$0.589012\pi$
$600$	−7416.66	+	7416.66i	−0.504640	+	0.504640i
$601$			21642.2i			1.46889i	0.678668	+	0.734445i	$0.262558\pi$
$601$			21642.2i			1.46889i	−0.678668	+	0.734445i	$0.737442\pi$
$602$	5745.38			0.388977
$603$	1182.65	+	1182.65i	0.0798692	+	0.0798692i
$604$	−1711.43	+	1711.43i	−0.115293	+	0.115293i
$605$	2711.00	+	5669.74i	0.182178	+	0.381005i
$606$	11276.2	−	11276.2i	0.755883	−	0.755883i
$607$			3287.84i			0.219851i	0.993940	+	0.109925i	$0.0350612\pi$
$607$			3287.84i			0.219851i	−0.993940	+	0.109925i	$0.964939\pi$
$608$			2596.61i			0.173201i
$609$	−115.536	+	115.536i	−0.00768759	+	0.00768759i
$610$			3408.51i			0.226240i
$611$	5921.03	−	7959.08i	0.392045	−	0.526988i
$612$		−	899.181i		−	0.0593909i
$613$	−10066.8	+	10066.8i	−0.663283	+	0.663283i	−0.956152	−	0.292870i	$-0.905390\pi$
$613$	−10066.8	+	10066.8i	−0.663283	+	0.663283i	0.292870	+	0.956152i	$0.405390\pi$
$614$	21033.4			1.38248
$615$	3499.33			0.229441
$616$	17396.4	+	2980.66i	1.13786	+	0.194958i
$617$	20807.5	+	20807.5i	1.35766	+	1.35766i	0.876789	+	0.480876i	$0.159681\pi$
$617$	20807.5	+	20807.5i	1.35766	+	1.35766i	0.480876	+	0.876789i	$0.340319\pi$
$618$	6372.48	+	6372.48i	0.414788	+	0.414788i
$619$	1415.01	−	1415.01i	0.0918806	−	0.0918806i	−0.659673	−	0.751553i	$-0.729305\pi$
$619$	1415.01	−	1415.01i	0.0918806	−	0.0918806i	0.751553	+	0.659673i	$0.229305\pi$
$620$	−3277.72			−0.212317
$621$		−	16342.2i		−	1.05602i
$622$	10584.3	+	10584.3i	0.682299	+	0.682299i
$623$	−13948.6			−0.897011
$624$	−4261.69	+	625.755i	−0.273404	+	0.0401446i
$625$	−7761.71			−0.496749
$626$	−9246.69	+	9246.69i	−0.590371	+	0.590371i
$627$	1544.65	+	2183.41i	0.0983848	+	0.139070i
$628$			1149.83i			0.0730625i
$629$	4532.99	−	4532.99i	0.287349	−	0.287349i
$630$	1300.91	+	1300.91i	0.0822688	+	0.0822688i
$631$	−11767.0	+	11767.0i	−0.742374	+	0.742374i	−0.973034	−	0.230661i	$-0.925911\pi$
$631$	−11767.0	+	11767.0i	−0.742374	+	0.742374i	0.230661	+	0.973034i	$0.425911\pi$
$632$	1097.03	−	1097.03i	0.0690465	−	0.0690465i
$633$		−	18601.9i		−	1.16802i
$634$	430.091			0.0269418
$635$	6847.49	+	6847.49i	0.427928	+	0.427928i
$636$		−	4615.61i		−	0.287769i
$637$	−359.717	−	2449.85i	−0.0223744	−	0.152381i
$638$	121.838	−	86.1942i	0.00756053	−	0.00534868i
$639$	−1466.90	−	1466.90i	−0.0908131	−	0.0908131i
$640$		−	816.032i		−	0.0504008i
$641$		−	3816.63i		−	0.235176i	−0.993062	−	0.117588i	$-0.962484\pi$
$641$		−	3816.63i		−	0.235176i	0.993062	−	0.117588i	$-0.0375163\pi$
$642$	−1244.99	−	1244.99i	−0.0765353	−	0.0765353i
$643$	9679.87	+	9679.87i	0.593681	+	0.593681i	0.938624	−	0.344943i	$-0.112102\pi$
$643$	9679.87	+	9679.87i	0.593681	+	0.593681i	−0.344943	+	0.938624i	$0.612102\pi$
$644$	5455.23	+	5455.23i	0.333798	+	0.333798i
$645$	−1935.60	−	1935.60i	−0.118162	−	0.118162i
$646$		−	967.942i		−	0.0589523i
$647$		−	13494.7i		−	0.819989i	−0.912088	−	0.409994i	$-0.865531\pi$
$647$		−	13494.7i		−	0.819989i	0.912088	−	0.409994i	$-0.134469\pi$
$648$	6681.61	+	6681.61i	0.405060	+	0.405060i
$649$	13818.4	+	19532.7i	0.835778	+	1.18140i
$650$	−8080.22	−	6011.15i	−0.487588	−	0.362733i
$651$			16007.4i			0.963716i
$652$	7950.18	+	7950.18i	0.477536	+	0.477536i
$653$	−17789.4			−1.06608			−0.533041	−	0.846089i	$-0.678951\pi$
$653$	−17789.4			−1.06608			−0.533041	+	0.846089i	$0.678951\pi$
$654$			12347.7i			0.738275i
$655$	4341.25	−	4341.25i	0.258972	−	0.258972i
$656$	−2730.33	+	2730.33i	−0.162502	+	0.162502i
$657$	−4091.10	−	4091.10i	−0.242936	−	0.242936i
$658$	−6228.63	+	6228.63i	−0.369023	+	0.369023i
$659$		−	3649.16i		−	0.215707i	−0.994167	−	0.107854i	$-0.965602\pi$
$659$		−	3649.16i		−	0.215707i	0.994167	−	0.107854i	$-0.0343978\pi$
$660$	−1514.01	−	2140.10i	−0.0892923	−	0.126217i
$661$	16512.6	−	16512.6i	0.971656	−	0.971656i	−0.0279529	−	0.999609i	$-0.508899\pi$
$661$	16512.6	−	16512.6i	0.971656	−	0.971656i	0.999609	+	0.0279529i	$0.00889886\pi$
$662$	9796.05			0.575128
$663$	−5162.61	+	758.039i	−0.302412	+	0.0444039i
$664$	−19931.5			−1.16490
$665$	−1159.49	−	1159.49i	−0.0676134	−	0.0676134i
$666$		−	4736.48i		−	0.275578i
$667$	209.261			0.0121478
$668$	2028.56	−	2028.56i	0.117496	−	0.117496i
$669$	−3457.94	−	3457.94i	−0.199838	−	0.199838i
$670$	−1247.84	−	1247.84i	−0.0719526	−	0.0719526i
$671$	12408.4	+	2126.03i	0.713890	+	0.122317i
$672$	−12429.6			−0.713514
$673$	16268.1			0.931781			0.465891	−	0.884842i	$-0.345734\pi$
$673$	16268.1			0.931781			0.465891	+	0.884842i	$0.345734\pi$
$674$	−16252.9	+	16252.9i	−0.928842	+	0.928842i
$675$			15684.4i			0.894359i
$676$	2288.52	+	7624.96i	0.130207	+	0.433828i
$677$			9140.17i			0.518885i	0.965759	+	0.259442i	$0.0835388\pi$
$677$			9140.17i			0.518885i	−0.965759	+	0.259442i	$0.916461\pi$
$678$	−13604.9	+	13604.9i	−0.770638	+	0.770638i
$679$			26790.4i			1.51417i
$680$			3043.36i			0.171629i
$681$	18492.5	−	18492.5i	1.04058	−	1.04058i
$682$	2469.22	−	14411.4i	0.138638	−	0.809148i
$683$	−22526.6	+	22526.6i	−1.26202	+	1.26202i	−0.311903	+	0.950114i	$0.600966\pi$
$683$	−22526.6	+	22526.6i	−1.26202	+	1.26202i	−0.950114	+	0.311903i	$0.899034\pi$
$684$	418.703	+	418.703i	0.0234057	+	0.0234057i
$685$	5122.20			0.285707
$686$		−	12077.3i		−	0.672177i
$687$	−12454.9	+	12454.9i	−0.691681	+	0.691681i
$688$	3020.48			0.167376
$689$	14065.2	−	2065.23i	0.777711	−	0.114193i
$690$			4439.38i			0.244934i
$691$	−22863.9	−	22863.9i	−1.25873	−	1.25873i	−0.951700	−	0.307031i	$-0.900665\pi$
$691$	−22863.9	−	22863.9i	−1.25873	−	1.25873i	−0.307031	−	0.951700i	$-0.599335\pi$
$692$			14542.0i			0.798852i
$693$	5547.26	−	3924.40i	0.304074	−	0.215117i
$694$	7054.81	+	7054.81i	0.385874	+	0.385874i
$695$	−5185.32	+	5185.32i	−0.283008	+	0.283008i
$696$	−141.209	+	141.209i	−0.00769041	+	0.00769041i
$697$	−3307.52	+	3307.52i	−0.179743	+	0.179743i
$698$	−6024.70			−0.326702
$699$	14514.6			0.785400
$700$	−5235.64	−	5235.64i	−0.282698	−	0.282698i
$701$	−20440.5			−1.10132			−0.550662	−	0.834729i	$-0.685625\pi$
$701$	−20440.5			−1.10132			−0.550662	+	0.834729i	$0.685625\pi$
$702$	−8937.89	+	12014.4i	−0.480540	+	0.645944i
$703$			4221.58i			0.226486i
$704$	17484.8	+	2995.83i	0.936058	+	0.160383i
$705$	4196.81			0.224200
$706$	17992.5			0.959146
$707$	25534.5	+	25534.5i	1.35831	+	1.35831i
$708$	−7057.33	−	7057.33i	−0.374620	−	0.374620i
$709$	−1512.41	+	1512.41i	−0.0801127	+	0.0801127i	−0.746028	−	0.665915i	$-0.768041\pi$
$709$	−1512.41	+	1512.41i	−0.0801127	+	0.0801127i	0.665915	+	0.746028i	$0.268041\pi$
$710$	1547.76	+	1547.76i	0.0818117	+	0.0818117i
$711$		−	597.291i		−	0.0315051i
$712$	−17048.1			−0.897339
$713$	14496.5	−	14496.5i	0.761426	−	0.761426i
$714$	4633.39			0.242858
$715$	5844.14	−	5571.26i	0.305676	−	0.291403i
$716$	2654.56			0.138555
$717$	8826.80	−	8826.80i	0.459753	−	0.459753i
$718$	6774.77			0.352134
$719$		−	19141.0i		−	0.992821i	−0.868088	−	0.496410i	$-0.834651\pi$
$719$		−	19141.0i		−	0.992821i	0.868088	−	0.496410i	$-0.165349\pi$
$720$	683.917	+	683.917i	0.0354001	+	0.0354001i
$721$	−14430.2	+	14430.2i	−0.745366	+	0.745366i
$722$	−9695.53	−	9695.53i	−0.499765	−	0.499765i
$723$	3752.59	+	3752.59i	0.193029	+	0.193029i
$724$	8049.00			0.413175
$725$	−200.837			−0.0102882
$726$	10550.1	−	5044.55i	0.539326	−	0.257880i
$727$		−	14794.3i		−	0.754734i	−0.926064	−	0.377367i	$-0.876830\pi$
$727$		−	14794.3i		−	0.754734i	0.926064	−	0.377367i	$-0.123170\pi$
$728$	−3294.26	−	22435.5i	−0.167711	−	1.14219i
$729$	20954.6			1.06460
$730$	4316.61	+	4316.61i	0.218856	+	0.218856i
$731$	3659.01			0.185135
$732$	−5251.39			−0.265160
$733$	−13964.6	+	13964.6i	−0.703677	+	0.703677i	−0.965198	−	0.261521i	$-0.915776\pi$
$733$	−13964.6	+	13964.6i	−0.703677	+	0.703677i	0.261521	+	0.965198i	$0.415776\pi$
$734$	−3468.19	+	3468.19i	−0.174405	+	0.174405i
$735$	740.740	−	740.740i	0.0371736	−	0.0371736i
$736$	11256.4	+	11256.4i	0.563743	+	0.563743i
$737$	−5320.97	+	3764.31i	−0.265944	+	0.188142i
$738$			3455.99i			0.172380i
$739$	7636.17	+	7636.17i	0.380110	+	0.380110i	0.871142	−	0.491032i	$-0.163380\pi$
$739$	7636.17	+	7636.17i	0.380110	+	0.380110i	−0.491032	+	0.871142i	$0.663380\pi$
$740$		−	4137.86i		−	0.205555i
$741$	2050.99	−	2756.95i	0.101680	−	0.136679i
$742$	−12623.4			−0.624555
$743$	18533.5	−	18533.5i	0.915110	−	0.915110i	−0.0815586	−	0.996669i	$-0.525990\pi$
$743$	18533.5	−	18533.5i	0.915110	−	0.915110i	0.996669	+	0.0815586i	$0.0259898\pi$
$744$			19564.4i			0.964068i
$745$	8313.28			0.408826
$746$	−12877.3	−	12877.3i	−0.631998	−	0.631998i
$747$	−5425.97	+	5425.97i	−0.265764	+	0.265764i
$748$	3453.83	+	591.773i	0.168829	+	0.0289269i
$749$	2819.22	−	2819.22i	0.137533	−	0.137533i
$750$		−	9446.24i		−	0.459904i
$751$		−	31347.8i		−	1.52317i	−0.648067	−	0.761584i	$-0.724422\pi$
$751$		−	31347.8i		−	1.52317i	0.648067	−	0.761584i	$-0.275578\pi$
$752$	−3274.54	+	3274.54i	−0.158790	+	0.158790i
$753$			454.038i			0.0219735i
$754$	−153.843	−	114.449i	−0.00743054	−	0.00552783i
$755$		−	3153.79i		−	0.152024i
$756$	−7784.79	+	7784.79i	−0.374511	+	0.374511i
$757$	13615.1			0.653700			0.326850	−	0.945076i	$-0.394013\pi$
$757$	13615.1			0.653700			0.326850	+	0.945076i	$0.394013\pi$
$758$	−23316.5			−1.11727
$759$	16161.2	+	2769.03i	0.772877	+	0.132423i
$760$	−1417.14	−	1417.14i	−0.0676382	−	0.0676382i
$761$	14164.2	+	14164.2i	0.674706	+	0.674706i	0.958797	−	0.284091i	$-0.0916918\pi$
$761$	14164.2	+	14164.2i	0.674706	+	0.674706i	−0.284091	+	0.958797i	$0.591692\pi$
$762$	12741.6	−	12741.6i	0.605748	−	0.605748i
$763$	−27960.8			−1.32667
$764$		−	8012.15i		−	0.379410i
$765$	828.497	+	828.497i	0.0391560	+	0.0391560i
$766$	−3427.95			−0.161693
$767$	18348.1	−	24663.7i	0.863772	−	1.16109i
$768$	−17855.5			−0.838941
$769$	8451.42	−	8451.42i	0.396315	−	0.396315i	−0.480616	−	0.876931i	$-0.659587\pi$
$769$	8451.42	−	8451.42i	0.396315	−	0.396315i	0.876931	+	0.480616i	$0.159587\pi$
$770$	−5853.05	+	4140.73i	−0.273934	+	0.193794i
$771$			26475.2i			1.23668i
$772$	10030.1	−	10030.1i	0.467607	−	0.467607i
$773$	12398.8	+	12398.8i	0.576913	+	0.576913i	0.934052	−	0.357138i	$-0.116247\pi$
$773$	12398.8	+	12398.8i	0.576913	+	0.576913i	−0.357138	+	0.934052i	$0.616247\pi$
$774$	1911.63	−	1911.63i	0.0887753	−	0.0887753i
$775$	−13912.9	+	13912.9i	−0.644861	+	0.644861i
$776$			32743.5i			1.51472i
$777$	−20208.0			−0.933024
$778$	−2066.74	−	2066.74i	−0.0952392	−	0.0952392i
$779$		−	3080.29i		−	0.141672i
$780$	−2010.32	+	2702.28i	−0.0922831	+	0.124047i
$781$	6599.87	−	4669.07i	0.302384	−	0.213921i
$782$	−4196.05	−	4196.05i	−0.191880	−	0.191880i
$783$			298.622i			0.0136295i
$784$			1155.92i			0.0526565i
$785$	−1059.44	−	1059.44i	−0.0481697	−	0.0481697i
$786$	−8078.07	−	8078.07i	−0.366584	−	0.366584i
$787$	7425.56	+	7425.56i	0.336331	+	0.336331i	0.854984	−	0.518654i	$-0.173567\pi$
$787$	7425.56	+	7425.56i	0.336331	+	0.336331i	−0.518654	+	0.854984i	$0.673567\pi$
$788$	1200.03	+	1200.03i	0.0542503	+	0.0542503i
$789$		−	13969.2i		−	0.630313i
$790$			630.215i			0.0283823i
$791$	−30807.7	−	30807.7i	−1.38482	−	1.38482i
$792$	6779.94	−	4796.46i	0.304185	−	0.215195i
$793$	−2349.71	−	16002.6i	−0.105221	−	0.716609i
$794$		−	22443.9i		−	1.00315i
$795$	4252.79	+	4252.79i	0.189724	+	0.189724i
$796$	−9248.64			−0.411821
$797$		−	14293.6i		−	0.635263i	−0.948214	−	0.317632i	$-0.897112\pi$
$797$		−	14293.6i		−	0.635263i	0.948214	−	0.317632i	$-0.102888\pi$
$798$	−2157.54	+	2157.54i	−0.0957093	+	0.0957093i
$799$	−3966.77	+	3966.77i	−0.175637	+	0.175637i
$800$	−10803.3	−	10803.3i	−0.477441	−	0.477441i
$801$	−4641.03	+	4641.03i	−0.204723	+	0.204723i
$802$		−	13427.8i		−	0.591210i
$803$	18406.7	−	13021.8i	0.808914	−	0.572265i
$804$	1922.51	−	1922.51i	0.0843304	−	0.0843304i
$805$	−10052.8			−0.440142
$806$	−18585.8	+	2729.00i	−0.812230	+	0.119262i
$807$	23528.6			1.02633
$808$	31208.6	+	31208.6i	1.35881	+	1.35881i
$809$		−	25787.0i		−	1.12067i	−0.828266	−	0.560335i	$-0.810672\pi$
$809$		−	25787.0i		−	1.12067i	0.828266	−	0.560335i	$-0.189328\pi$
$810$	−3838.42			−0.166504
$811$	−5206.55	+	5206.55i	−0.225434	+	0.225434i	−0.810782	−	0.585348i	$-0.800958\pi$
$811$	−5206.55	+	5206.55i	−0.225434	+	0.225434i	0.585348	+	0.810782i	$0.300958\pi$
$812$	−99.6837	−	99.6837i	−0.00430814	−	0.00430814i
$813$	−16953.6	−	16953.6i	−0.731349	−	0.731349i
$814$	18193.2	+	3117.19i	0.783379	+	0.134223i
$815$	−14650.5			−0.629672
$816$	2435.88			0.104501
$817$	−1703.82	+	1703.82i	−0.0729609	+	0.0729609i
$818$		−	20421.8i		−	0.872897i
$819$	−7004.44	−	5210.84i	−0.298846	−	0.222322i
$820$			3019.20i			0.128579i
$821$	−14058.6	+	14058.6i	−0.597622	+	0.597622i	−0.939679	−	0.342057i	$-0.888876\pi$
$821$	−14058.6	+	14058.6i	−0.597622	+	0.597622i	0.342057	+	0.939679i	$0.388876\pi$
$822$		−	9531.23i		−	0.404428i
$823$			15107.5i			0.639873i	0.947439	+	0.319936i	$0.103662\pi$
$823$			15107.5i			0.639873i	−0.947439	+	0.319936i	$0.896338\pi$
$824$	−17636.8	+	17636.8i	−0.745639	+	0.745639i
$825$	−15510.6	−	2657.57i	−0.654559	−	0.112151i
$826$	−19301.3	+	19301.3i	−0.813050	+	0.813050i
$827$	25618.1	+	25618.1i	1.07718	+	1.07718i	0.996761	+	0.0804214i	$0.0256266\pi$
$827$	25618.1	+	25618.1i	1.07718	+	1.07718i	0.0804214	+	0.996761i	$0.474373\pi$
$828$	3630.18			0.152364
$829$			1633.92i			0.0684539i	0.999414	+	0.0342270i	$0.0108969\pi$
$829$			1633.92i			0.0684539i	−0.999414	+	0.0342270i	$0.989103\pi$
$830$	5725.07	−	5725.07i	0.239422	−	0.239422i
$831$	−8225.26			−0.343359
$832$	−3311.01	−	22549.6i	−0.137967	−	0.939624i
$833$			1400.27i			0.0582433i
$834$	9648.68	+	9648.68i	0.400607	+	0.400607i
$835$			3738.19i			0.154928i
$836$	−1883.83	+	1332.71i	−0.0779351	+	0.0551350i
$837$	20686.9	+	20686.9i	0.854296	+	0.854296i
$838$	5811.74	−	5811.74i	0.239574	−	0.239574i
$839$	1398.75	−	1398.75i	0.0575570	−	0.0575570i	−0.677742	−	0.735299i	$-0.737042\pi$
$839$	1398.75	−	1398.75i	0.0575570	−	0.0575570i	0.735299	+	0.677742i	$0.237042\pi$
$840$	6783.63	−	6783.63i	0.278640	−	0.278640i
$841$	24385.2			0.999843
$842$	8804.79			0.360372
$843$	−17395.2	−	17395.2i	−0.710701	−	0.710701i
$844$	16049.6			0.654562
$845$	−9134.19	−	4916.94i	−0.371865	−	0.200175i
$846$			4144.84i			0.168443i
$847$	11423.2	+	23890.2i	0.463405	+	0.969159i
$848$	−6636.42			−0.268745
$849$	969.194			0.0391786
$850$	4027.15	+	4027.15i	0.162506	+	0.162506i
$851$	18300.6	+	18300.6i	0.737177	+	0.737177i
$852$	−2384.59	+	2384.59i	−0.0958857	+	0.0958857i
$853$	−13573.4	−	13573.4i	−0.544833	−	0.544833i	0.380109	−	0.924942i	$-0.375887\pi$
$853$	−13573.4	−	13573.4i	−0.544833	−	0.544833i	−0.924942	+	0.380109i	$0.875887\pi$
$854$			14362.2i			0.575486i
$855$	−771.579			−0.0308625
$856$	3445.68	−	3445.68i	0.137583	−	0.137583i
$857$	−6349.49			−0.253086			−0.126543	−	0.991961i	$-0.540388\pi$
$857$	−6349.49			−0.253086			−0.126543	+	0.991961i	$0.540388\pi$
$858$	−10366.8	−	10874.6i	−0.412492	−	0.432695i
$859$	1347.93			0.0535401			0.0267700	−	0.999642i	$-0.491478\pi$
$859$	1347.93			0.0535401			0.0267700	+	0.999642i	$0.491478\pi$
$860$	1670.03	−	1670.03i	0.0662180	−	0.0662180i
$861$	14744.9			0.583629
$862$		−	23941.6i		−	0.946002i
$863$	2776.75	+	2776.75i	0.109527	+	0.109527i	0.759746	−	0.650220i	$-0.225323\pi$
$863$	2776.75	+	2776.75i	0.109527	+	0.109527i	−0.650220	+	0.759746i	$0.725323\pi$
$864$	−16063.2	+	16063.2i	−0.632502	+	0.632502i
$865$	−13398.9	−	13398.9i	−0.526678	−	0.526678i
$866$	1992.73	+	1992.73i	0.0781936	+	0.0781936i
$867$	−17682.8			−0.692664
$868$	−13811.1			−0.540068
$869$	2294.24	+	393.092i	0.0895590	+	0.0153449i
$870$		−	81.1212i		−	0.00316123i
$871$	6718.71	+	4998.27i	0.261372	+	0.194443i
$872$	−34174.0			−1.32715
$873$	8913.81	+	8913.81i	0.345575	+	0.345575i
$874$	3907.78			0.151239
$875$	21390.6			0.826439
$876$	−6650.48	+	6650.48i	−0.256505	+	0.256505i
$877$	−14426.1	+	14426.1i	−0.555456	+	0.555456i	−0.928010	−	0.372555i	$-0.878482\pi$
$877$	−14426.1	+	14426.1i	−0.555456	+	0.555456i	0.372555	+	0.928010i	$0.378482\pi$
$878$	3718.16	−	3718.16i	0.142918	−	0.142918i
$879$	20095.3	+	20095.3i	0.771103	+	0.771103i
$880$	−3077.09	+	2176.88i	−0.117873	+	0.0833893i
$881$		−	10038.0i		−	0.383868i	−0.981408	−	0.191934i	$-0.938524\pi$
$881$		−	10038.0i		−	0.383868i	0.981408	−	0.191934i	$-0.0614759\pi$
$882$	731.566	+	731.566i	0.0279287	+	0.0279287i
$883$			32383.4i			1.23419i	0.786889	+	0.617094i	$0.211690\pi$
$883$			32383.4i			1.23419i	−0.786889	+	0.617094i	$0.788310\pi$
$884$	−654.033	−	4454.28i	−0.0248841	−	0.169472i
$885$	13005.1			0.493969
$886$	−7564.99	+	7564.99i	−0.286852	+	0.286852i
$887$			26942.0i			1.01987i	0.860213	+	0.509934i	$0.170330\pi$
$887$			26942.0i			1.01987i	−0.860213	+	0.509934i	$0.829670\pi$
$888$	−24698.5			−0.933365
$889$	28852.8	+	28852.8i	1.08852	+	1.08852i
$890$	4896.86	−	4896.86i	0.184431	−	0.184431i
$891$	−2394.18	+	13973.4i	−0.0900204	+	0.525396i
$892$	2983.50	−	2983.50i	0.111990	−	0.111990i
$893$		−	3694.25i		−	0.138436i
$894$		−	15469.1i		−	0.578707i
$895$	−2445.89	+	2445.89i	−0.0913486	+	0.0913486i
$896$		−	3438.46i		−	0.128204i
$897$	−3060.36	−	20842.5i	−0.113916	−	0.775821i
$898$		−	9993.51i		−	0.371367i
$899$	−264.895	+	264.895i	−0.00982729	+	0.00982729i
$900$	−3484.05			−0.129039
$901$	−8039.35			−0.297258
$902$	−13274.7	−	2274.47i	−0.490022	−	0.0839596i
$903$	−8155.92	−	8155.92i	−0.300567	−	0.300567i
$904$	−37653.5	−	37653.5i	−1.38533	−	1.38533i
$905$	−7416.27	+	7416.27i	−0.272404	+	0.272404i
$906$	−5868.48			−0.215196
$907$		−	47391.8i		−	1.73497i	−0.497464	−	0.867485i	$-0.665735\pi$
$907$		−	47391.8i		−	1.73497i	0.497464	−	0.867485i	$-0.334265\pi$
$908$	15955.3	+	15955.3i	0.583143	+	0.583143i
$909$	16991.9			0.620007
$910$	7390.55	+	5498.08i	0.269224	+	0.200285i
$911$	17806.5			0.647592			0.323796	−	0.946127i	$-0.395041\pi$
$911$	17806.5			0.647592			0.323796	+	0.946127i	$0.395041\pi$
$912$	−1134.27	+	1134.27i	−0.0411836	+	0.0411836i
$913$	−17270.6	−	24412.6i	−0.626040	−	0.884927i
$914$			33984.1i			1.22986i
$915$	4838.59	−	4838.59i	0.174818	−	0.174818i
$916$	−10746.1	−	10746.1i	−0.387620	−	0.387620i
$917$	18292.4	−	18292.4i	0.658745	−	0.658745i
$918$	5987.91	−	5987.91i	0.215284	−	0.215284i
$919$		−	39712.1i		−	1.42544i	−0.701447	−	0.712722i	$-0.747462\pi$
$919$		−	39712.1i		−	1.42544i	0.701447	−	0.712722i	$-0.252538\pi$
$920$	−12286.7			−0.440303
$921$	−29858.2	−	29858.2i	−1.06825	−	1.06825i
$922$		−	21354.3i		−	0.762763i
$923$	−8333.56	−	6199.61i	−0.297186	−	0.221086i
$924$	−6379.50	−	9017.62i	−0.227132	−	0.321058i
$925$	−17564.0	−	17564.0i	−0.624324	−	0.624324i
$926$		−	17581.2i		−	0.623925i
$927$			9602.57i			0.340226i
$928$	−205.688	−	205.688i	−0.00727591	−	0.00727591i
$929$	−8557.17	−	8557.17i	−0.302209	−	0.302209i	0.539669	−	0.841877i	$-0.318549\pi$
$929$	−8557.17	−	8557.17i	−0.302209	−	0.302209i	−0.841877	+	0.539669i	$0.818549\pi$
$930$	−5619.64	−	5619.64i	−0.198145	−	0.198145i
$931$	−652.038	−	652.038i	−0.0229535	−	0.0229535i
$932$			12523.2i			0.440140i
$933$		−	30050.0i		−	1.05444i
$934$	−10739.0	−	10739.0i	−0.376222	−	0.376222i
$935$	−3727.58	+	2637.07i	−0.130380	+	0.0922368i
$936$	−8560.92	−	6368.76i	−0.298955	−	0.222403i
$937$			28201.7i			0.983255i	0.870805	+	0.491628i	$0.163598\pi$
$937$			28201.7i			0.983255i	−0.870805	+	0.491628i	$0.836402\pi$
$938$	−5257.94	−	5257.94i	−0.183025	−	0.183025i
$939$	26252.5			0.912372
$940$			3620.99i			0.125642i
$941$	23843.0	−	23843.0i	0.825994	−	0.825994i	−0.160966	−	0.986960i	$-0.551461\pi$
$941$	23843.0	−	23843.0i	0.825994	−	0.825994i	0.986960	+	0.160966i	$0.0514609\pi$
$942$	−1971.38	+	1971.38i	−0.0681859	+	0.0681859i
$943$	−13353.1	−	13353.1i	−0.461121	−	0.461121i
$944$	−10147.2	+	10147.2i	−0.349854	+	0.349854i
$945$		−	14345.7i		−	0.493825i
$946$	6084.63	+	8600.81i	0.209121	+	0.295599i
$947$	15129.0	−	15129.0i	0.519140	−	0.519140i	−0.398171	−	0.917311i	$-0.630355\pi$
$947$	15129.0	−	15129.0i	0.519140	−	0.519140i	0.917311	+	0.398171i	$0.130355\pi$
$948$	−970.954			−0.0332649
$949$	−23241.8	−	17290.4i	−0.795007	−	0.591433i
$950$	−3750.48			−0.128086
$951$	−610.541	−	610.541i	−0.0208182	−	0.0208182i
$952$			12823.6i			0.436570i
$953$	37307.9			1.26812			0.634062	−	0.773283i	$-0.281387\pi$
$953$	37307.9			1.26812			0.634062	+	0.773283i	$0.281387\pi$
$954$	−4200.12	+	4200.12i	−0.142541	+	0.142541i
$955$	7382.32	+	7382.32i	0.250143	+	0.250143i
$956$	7615.73	+	7615.73i	0.257647	+	0.257647i
$957$	−295.314	−	50.5987i	−0.00997509	−	0.00170912i
$958$	3072.34			0.103615
$959$	21583.1			0.726750
$960$	6818.14	−	6818.14i	0.229223	−	0.229223i
$961$			6909.98i			0.231948i
$962$	−3445.15	−	23463.1i	−0.115464	−	0.786363i
$963$		−	1876.04i		−	0.0627775i
$964$	−3237.71	+	3237.71i	−0.108174	+	0.108174i
$965$			18483.4i			0.616581i
$966$			18705.9i			0.623037i
$967$	3676.52	−	3676.52i	0.122264	−	0.122264i	−0.643327	−	0.765591i	$-0.722447\pi$
$967$	3676.52	−	3676.52i	0.122264	−	0.122264i	0.765591	+	0.643327i	$0.222447\pi$
$968$	13961.5	+	29198.9i	0.463575	+	0.969514i
$969$	−1374.05	+	1374.05i	−0.0455531	+	0.0455531i
$970$	−9405.17	−	9405.17i	−0.311322	−	0.311322i
$971$	−13979.6			−0.462026			−0.231013	−	0.972951i	$-0.574204\pi$
$971$	−13979.6			−0.462026			−0.231013	+	0.972951i	$0.574204\pi$
$972$			9027.03i			0.297883i
$973$	−21849.0	+	21849.0i	−0.719884	+	0.719884i
$974$	26815.2			0.882152
$975$	2937.17	+	20003.5i	0.0964766	+	0.657053i
$976$			7550.56i			0.247631i
$977$	13666.0	+	13666.0i	0.447505	+	0.447505i	0.894524	−	0.447019i	$-0.147514\pi$
$977$	13666.0	+	13666.0i	0.447505	+	0.447505i	−0.447019	+	0.894524i	$0.647514\pi$
$978$			27261.1i			0.891324i
$979$	−14772.2	−	20881.0i	−0.482249	−	0.681674i
$980$	639.107	+	639.107i	0.0208322	+	0.0208322i
$981$	−9303.23	+	9303.23i	−0.302782	+	0.302782i
$982$	4419.10	−	4419.10i	0.143604	−	0.143604i
$983$	10216.0	−	10216.0i	0.331474	−	0.331474i	−0.521672	−	0.853146i	$-0.674692\pi$
$983$	10216.0	−	10216.0i	0.331474	−	0.331474i	0.853146	+	0.521672i	$0.174692\pi$
$984$	18021.4			0.583842
$985$	−2211.39			−0.0715338
$986$	76.6747	+	76.6747i	0.00247649	+	0.00247649i
$987$	17683.8			0.570296
$988$	2378.69	+	1769.58i	0.0765952	+	0.0569818i
$989$			14772.2i			0.474952i
$990$	−569.730	+	3325.17i	−0.0182901	+	0.106748i
$991$	53045.4			1.70034			0.850172	−	0.526504i	$-0.176498\pi$
$991$	53045.4			1.70034			0.850172	+	0.526504i	$0.176498\pi$
$992$	−28498.0			−0.912108
$993$	−13906.1	−	13906.1i	−0.444407	−	0.444407i
$994$	6521.69	+	6521.69i	0.208104	+	0.208104i
$995$	8521.61	−	8521.61i	0.271511	−	0.271511i
$996$	8820.45	+	8820.45i	0.280609	+	0.280609i
$997$			2039.03i			0.0647712i	0.999475	+	0.0323856i	$0.0103105\pi$
$997$			2039.03i			0.0647712i	−0.999475	+	0.0323856i	$0.989690\pi$
$998$	35960.6			1.14059
$999$	−26115.6	+	26115.6i	−0.827089	+	0.827089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.15	✓	80
11.10	odd	2	inner	143.4.g.a.21.26	yes	80
13.5	odd	4	inner	143.4.g.a.109.26	yes	80
143.109	even	4	inner	143.4.g.a.109.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.15	✓	80	1.1	even	1	trivial
143.4.g.a.21.26	yes	80	11.10	odd	2	inner
143.4.g.a.109.15	yes	80	143.109	even	4	inner
143.4.g.a.109.26	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)

\(f(q)\)	\(=\)	\(q+(-1.47926 + 1.47926i) q^{2} +4.19980 q^{3} +3.62357i q^{4} +(-3.33873 - 3.33873i) q^{5} +(-6.21261 + 6.21261i) q^{6} +(-14.0682 - 14.0682i) q^{7} +(-17.1943 - 17.1943i) q^{8} -9.36165 q^{9} +O(q^{10})\)	\(q+(-1.47926 + 1.47926i) q^{2} +4.19980 q^{3} +3.62357i q^{4} +(-3.33873 - 3.33873i) q^{5} +(-6.21261 + 6.21261i) q^{6} +(-14.0682 - 14.0682i) q^{7} +(-17.1943 - 17.1943i) q^{8} -9.36165 q^{9} +9.87770 q^{10} +(6.16113 - 35.9589i) q^{11} +15.2183i q^{12} +(-46.3749 + 6.80934i) q^{13} +41.6210 q^{14} +(-14.0220 - 14.0220i) q^{15} +21.8812 q^{16} +26.5068 q^{17} +(13.8483 - 13.8483i) q^{18} +(-12.3429 + 12.3429i) q^{19} +(12.0981 - 12.0981i) q^{20} +(-59.0836 - 59.0836i) q^{21} +(44.0786 + 62.3065i) q^{22} +107.013i q^{23} +(-72.2127 - 72.2127i) q^{24} -102.706i q^{25} +(58.5278 - 78.6734i) q^{26} -152.712 q^{27} +(50.9770 - 50.9770i) q^{28} -1.95546i q^{29} +41.4844 q^{30} +(-135.464 - 135.464i) q^{31} +(105.186 - 105.186i) q^{32} +(25.8756 - 151.020i) q^{33} +(-39.2105 + 39.2105i) q^{34} +93.9396i q^{35} -33.9226i q^{36} +(171.012 - 171.012i) q^{37} -36.5167i q^{38} +(-194.766 + 28.5979i) q^{39} +114.814i q^{40} +(-124.780 + 124.780i) q^{41} +174.800 q^{42} +138.040 q^{43} +(130.300 + 22.3253i) q^{44} +(31.2560 + 31.2560i) q^{45} +(-158.301 - 158.301i) q^{46} +(-149.651 + 149.651i) q^{47} +91.8965 q^{48} +52.8270i q^{49} +(151.929 + 151.929i) q^{50} +111.323 q^{51} +(-24.6741 - 168.043i) q^{52} -303.294 q^{53} +(225.901 - 225.901i) q^{54} +(-140.627 + 99.4865i) q^{55} +483.785i q^{56} +(-51.8377 + 51.8377i) q^{57} +(2.89264 + 2.89264i) q^{58} +(-463.740 + 463.740i) q^{59} +(50.8097 - 50.8097i) q^{60} +345.071i q^{61} +400.773 q^{62} +(131.701 + 131.701i) q^{63} +486.246i q^{64} +(177.568 + 132.099i) q^{65} +(185.122 + 261.675i) q^{66} +(-126.329 - 126.329i) q^{67} +96.0493i q^{68} +449.435i q^{69} +(-138.961 - 138.961i) q^{70} +(156.692 + 156.692i) q^{71} +(160.967 + 160.967i) q^{72} +(437.006 + 437.006i) q^{73} +505.944i q^{74} -431.344i q^{75} +(-44.7254 - 44.7254i) q^{76} +(-592.552 + 419.200i) q^{77} +(245.805 - 330.413i) q^{78} +63.8018i q^{79} +(-73.0552 - 73.0552i) q^{80} -388.595 q^{81} -369.164i q^{82} +(579.595 - 579.595i) q^{83} +(214.094 - 214.094i) q^{84} +(-88.4990 - 88.4990i) q^{85} +(-204.198 + 204.198i) q^{86} -8.21256i q^{87} +(-724.224 + 512.351i) q^{88} +(495.749 - 495.749i) q^{89} -92.4716 q^{90} +(748.205 + 556.615i) q^{91} -387.771 q^{92} +(-568.922 - 568.922i) q^{93} -442.746i q^{94} +82.4191 q^{95} +(441.762 - 441.762i) q^{96} +(-952.162 - 952.162i) q^{97} +(-78.1449 - 78.1449i) q^{98} +(-57.6784 + 336.635i) 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

Related objects

Downloads

Learn more