LMFDB - Embedded newform 252.4.i.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.72803 + 2.15539i) q^{3} +(4.93620 - 8.54976i) q^{5} +(-6.20989 + 17.4481i) q^{7} +(17.7086 - 20.3815i) q^{9} +O(q^{10})$	\(q+(-4.72803 + 2.15539i) q^{3} +(4.93620 - 8.54976i) q^{5} +(-6.20989 + 17.4481i) q^{7} +(17.7086 - 20.3815i) q^{9} +(-19.2082 - 33.2696i) q^{11} +(26.0446 + 45.1105i) q^{13} +(-4.91047 + 51.0630i) q^{15} +(22.1423 - 38.3516i) q^{17} +(12.5408 + 21.7212i) q^{19} +(-8.24695 - 95.8801i) q^{21} +(-72.8656 + 126.207i) q^{23} +(13.7678 + 23.8465i) q^{25} +(-39.7967 + 134.533i) q^{27} +(-42.5752 + 73.7424i) q^{29} -151.013 q^{31} +(162.526 + 115.898i) q^{33} +(118.524 + 139.221i) q^{35} +(145.530 + 252.066i) q^{37} +(-220.370 - 157.148i) q^{39} +(153.439 + 265.764i) q^{41} +(-266.924 + 462.326i) q^{43} +(-86.8437 - 252.011i) q^{45} -465.799 q^{47} +(-265.874 - 216.702i) q^{49} +(-22.0269 + 229.053i) q^{51} +(-87.4354 + 151.443i) q^{53} -379.262 q^{55} +(-106.111 - 75.6685i) q^{57} +823.937 q^{59} -631.786 q^{61} +(245.651 + 435.549i) q^{63} +514.245 q^{65} +628.410 q^{67} +(72.4859 - 753.765i) q^{69} +559.983 q^{71} +(130.803 - 226.558i) q^{73} +(-116.493 - 83.0721i) q^{75} +(699.772 - 128.547i) q^{77} +582.313 q^{79} +(-101.812 - 721.855i) q^{81} +(-113.696 + 196.927i) q^{83} +(-218.598 - 378.623i) q^{85} +(42.3533 - 440.423i) q^{87} +(-154.511 - 267.622i) q^{89} +(-948.828 + 174.298i) q^{91} +(713.993 - 325.491i) q^{93} +247.615 q^{95} +(-15.4942 + 26.8368i) q^{97} +(-1018.23 - 197.665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−4.72803	+	2.15539i	−0.909910	+	0.414805i
$3$	−4.72803	+	2.15539i	−0.909910	+	0.414805i
$4$		0			0
$5$	4.93620	−	8.54976i	0.441507	−	0.764713i	−0.556294	−	0.830985i	$-0.687777\pi$
$5$	4.93620	−	8.54976i	0.441507	−	0.764713i	0.997802	+	0.0662721i	$0.0211105\pi$
$6$		0			0
$7$	−6.20989	+	17.4481i	−0.335303	+	0.942110i
$7$	−6.20989	+	17.4481i	−0.335303	+	0.942110i
$8$		0			0
$9$	17.7086	−	20.3815i	0.655874	−	0.754871i
$10$		0			0
$11$	−19.2082	−	33.2696i	−0.526499	−	0.911923i	−0.999523	−	0.0308733i	$-0.990171\pi$
$11$	−19.2082	−	33.2696i	−0.526499	−	0.911923i	0.473025	−	0.881049i	$-0.343162\pi$
$12$		0			0
$13$	26.0446	+	45.1105i	0.555651	+	0.962415i	0.997853	+	0.0654998i	$0.0208642\pi$
$13$	26.0446	+	45.1105i	0.555651	+	0.962415i	−0.442202	+	0.896916i	$0.645803\pi$
$14$		0			0
$15$	−4.91047	+	51.0630i	−0.0845253	+	0.878960i
$16$		0			0
$17$	22.1423	−	38.3516i	0.315900	−	0.547155i	−0.663729	−	0.747974i	$-0.731027\pi$
$17$	22.1423	−	38.3516i	0.315900	−	0.547155i	0.979628	+	0.200819i	$0.0643603\pi$
$18$		0			0
$19$	12.5408	+	21.7212i	0.151424	+	0.262273i	0.931751	−	0.363098i	$-0.118281\pi$
$19$	12.5408	+	21.7212i	0.151424	+	0.262273i	−0.780327	+	0.625371i	$0.784948\pi$
$20$		0			0
$21$	−8.24695	−	95.8801i	−0.0856968	−	0.996321i
$22$		0			0
$23$	−72.8656	+	126.207i	−0.660589	+	1.14417i	0.319873	+	0.947461i	$0.396360\pi$
$23$	−72.8656	+	126.207i	−0.660589	+	1.14417i	−0.980461	+	0.196712i	$0.936973\pi$
$24$		0			0
$25$	13.7678	+	23.8465i	0.110142	+	0.190772i
$26$		0			0
$27$	−39.7967	+	134.533i	−0.283662	+	0.958924i
$28$		0			0
$29$	−42.5752	+	73.7424i	−0.272621	+	0.472194i	−0.969532	−	0.244964i	$-0.921224\pi$
$29$	−42.5752	+	73.7424i	−0.272621	+	0.472194i	0.696911	+	0.717158i	$0.254557\pi$
$30$		0			0
$31$	−151.013			−0.874925			−0.437463	−	0.899237i	$-0.644123\pi$
$31$	−151.013			−0.874925			−0.437463	+	0.899237i	$0.644123\pi$
$32$		0			0
$33$	162.526	+	115.898i	0.857337	+	0.611373i
$34$		0			0
$35$	118.524	+	139.221i	0.572406	+	0.672359i
$36$		0			0
$37$	145.530	+	252.066i	0.646623	+	1.11998i	0.983924	+	0.178587i	$0.0571527\pi$
$37$	145.530	+	252.066i	0.646623	+	1.11998i	−0.337301	+	0.941397i	$0.609514\pi$
$38$		0			0
$39$	−220.370	−	157.148i	−0.904807	−	0.645225i
$40$		0			0
$41$	153.439	+	265.764i	0.584466	+	1.01233i	0.994942	+	0.100454i	$0.0320295\pi$
$41$	153.439	+	265.764i	0.584466	+	1.01233i	−0.410475	+	0.911872i	$0.634637\pi$
$42$		0			0
$43$	−266.924	+	462.326i	−0.946641	+	1.63963i	−0.194209	+	0.980960i	$0.562214\pi$
$43$	−266.924	+	462.326i	−0.946641	+	1.63963i	−0.752432	+	0.658670i	$0.771119\pi$
$44$		0			0
$45$	−86.8437	−	252.011i	−0.287687	−	0.834836i
$46$		0			0
$47$	−465.799			−1.44561			−0.722806	−	0.691051i	$-0.757148\pi$
$47$	−465.799			−1.44561			−0.722806	+	0.691051i	$0.757148\pi$
$48$		0			0
$49$	−265.874	−	216.702i	−0.775144	−	0.631784i
$50$		0			0
$51$	−22.0269	+	229.053i	−0.0604781	+	0.628898i
$52$		0			0
$53$	−87.4354	+	151.443i	−0.226607	+	0.392495i	−0.956800	−	0.290746i	$-0.906097\pi$
$53$	−87.4354	+	151.443i	−0.226607	+	0.392495i	0.730193	+	0.683241i	$0.239430\pi$
$54$		0			0
$55$	−379.262			−0.929812
$56$		0			0
$57$	−106.111	−	75.6685i	−0.246574	−	0.175834i
$58$		0			0
$59$	823.937			1.81809			0.909046	−	0.416696i	$-0.136812\pi$
$59$	823.937			1.81809			0.909046	+	0.416696i	$0.136812\pi$
$60$		0			0
$61$	−631.786			−1.32610			−0.663048	−	0.748577i	$-0.730738\pi$
$61$	−631.786			−1.32610			−0.663048	+	0.748577i	$0.730738\pi$
$62$		0			0
$63$	245.651	+	435.549i	0.491255	+	0.871016i
$64$		0			0
$65$	514.245			0.981296
$66$		0			0
$67$	628.410			1.14586			0.572929	−	0.819605i	$-0.305807\pi$
$67$	628.410			1.14586			0.572929	+	0.819605i	$0.305807\pi$
$68$		0			0
$69$	72.4859	−	753.765i	0.126468	−	1.31511i
$70$		0			0
$71$	559.983			0.936025			0.468013	−	0.883722i	$-0.344970\pi$
$71$	559.983			0.936025			0.468013	+	0.883722i	$0.344970\pi$
$72$		0			0
$73$	130.803	−	226.558i	0.209718	−	0.363242i	−0.741908	−	0.670502i	$-0.766079\pi$
$73$	130.803	−	226.558i	0.209718	−	0.363242i	0.951626	+	0.307260i	$0.0994122\pi$
$74$		0			0
$75$	−116.493	−	83.0721i	−0.179353	−	0.127898i
$76$		0			0
$77$	699.772	−	128.547i	1.03567	−	0.190250i
$78$		0			0
$79$	582.313			0.829309			0.414654	−	0.909979i	$-0.363903\pi$
$79$	582.313			0.829309			0.414654	+	0.909979i	$0.363903\pi$
$80$		0			0
$81$	−101.812	−	721.855i	−0.139660	−	0.990200i
$82$		0			0
$83$	−113.696	+	196.927i	−0.150358	+	0.260428i	−0.931359	−	0.364102i	$-0.881376\pi$
$83$	−113.696	+	196.927i	−0.150358	+	0.260428i	0.781001	+	0.624530i	$0.214709\pi$
$84$		0			0
$85$	−218.598	−	378.623i	−0.278944	−	0.483146i
$86$		0			0
$87$	42.3533	−	440.423i	0.0521925	−	0.542739i
$88$		0			0
$89$	−154.511	−	267.622i	−0.184024	−	0.318740i	0.759223	−	0.650831i	$-0.225579\pi$
$89$	−154.511	−	267.622i	−0.184024	−	0.318740i	−0.943247	+	0.332091i	$0.892246\pi$
$90$		0			0
$91$	−948.828	+	174.298i	−1.09301	+	0.200784i
$92$		0			0
$93$	713.993	−	325.491i	0.796104	−	0.362923i
$94$		0			0
$95$	247.615			0.267418
$96$		0			0
$97$	−15.4942	+	26.8368i	−0.0162186	+	0.0280914i	−0.874021	−	0.485889i	$-0.838496\pi$
$97$	−15.4942	+	26.8368i	−0.0162186	+	0.0280914i	0.857802	+	0.513980i	$0.171829\pi$
$98$		0			0
$99$	−1018.23	−	197.665i	−1.03370	−	0.200667i
$100$		0			0
$101$	−605.552	−	1048.85i	−0.596581	−	1.03331i	−0.993322	−	0.115378i	$-0.963192\pi$
$101$	−605.552	−	1048.85i	−0.596581	−	1.03331i	0.396740	−	0.917931i	$-0.370141\pi$
$102$		0			0
$103$	177.505	−	307.447i	0.169806	−	0.294113i	−0.768545	−	0.639795i	$-0.779019\pi$
$103$	177.505	−	307.447i	0.169806	−	0.294113i	0.938352	+	0.345682i	$0.112352\pi$
$104$		0			0
$105$	−860.460	−	402.774i	−0.799736	−	0.374350i
$106$		0			0
$107$	317.861	+	550.551i	0.287185	+	0.497419i	0.973137	−	0.230228i	$-0.0739473\pi$
$107$	317.861	+	550.551i	0.287185	+	0.497419i	−0.685952	+	0.727647i	$0.740614\pi$
$108$		0			0
$109$	−801.801	+	1388.76i	−0.704574	+	1.22036i	0.262271	+	0.964994i	$0.415529\pi$
$109$	−801.801	+	1388.76i	−0.704574	+	1.22036i	−0.966845	+	0.255364i	$0.917805\pi$
$110$		0			0
$111$	−1231.37	−	878.102i	−1.05294	−	0.750863i
$112$		0			0
$113$	173.026	+	299.691i	0.144044	+	0.249491i	0.929016	−	0.370040i	$-0.120656\pi$
$113$	173.026	+	299.691i	0.144044	+	0.249491i	−0.784972	+	0.619531i	$0.787323\pi$
$114$		0			0
$115$	719.359	+	1245.97i	0.583310	+	1.01032i
$116$		0			0
$117$	1380.63	+	268.016i	1.09094	+	0.211778i
$118$		0			0
$119$	531.662	+	624.501i	0.409558	+	0.481075i
$120$		0			0
$121$	−72.4088	+	125.416i	−0.0544018	+	0.0942266i
$122$		0			0
$123$	−1298.29	−	925.820i	−0.951730	−	0.678686i
$124$		0			0
$125$	1505.89			1.07753
$126$		0			0
$127$	−1786.72			−1.24839			−0.624194	−	0.781269i	$-0.714573\pi$
$127$	−1786.72			−1.24839			−0.624194	+	0.781269i	$0.714573\pi$
$128$		0			0
$129$	265.533	−	2761.22i	0.181232	−	1.88459i
$130$		0			0
$131$	597.314	−	1034.58i	0.398378	−	0.690012i	−0.595148	−	0.803616i	$-0.702906\pi$
$131$	597.314	−	1034.58i	0.398378	−	0.690012i	0.993526	+	0.113605i	$0.0362398\pi$
$132$		0			0
$133$	−456.872	+	83.9263i	−0.297863	+	0.0547168i
$134$		0			0
$135$	953.783	+	1004.34i	0.608063	+	0.640292i
$136$		0			0
$137$	−6.25151	−	10.8279i	−0.00389856	−	0.00675251i	0.864070	−	0.503372i	$-0.167908\pi$
$137$	−6.25151	−	10.8279i	−0.00389856	−	0.00675251i	−0.867968	+	0.496620i	$0.834574\pi$
$138$		0			0
$139$	−840.001	−	1454.92i	−0.512575	−	0.887806i	−0.999894	−	0.0145820i	$-0.995358\pi$
$139$	−840.001	−	1454.92i	−0.512575	−	0.887806i	0.487318	−	0.873224i	$-0.337975\pi$
$140$		0			0
$141$	2202.31	−	1003.98i	1.31538	−	0.599647i
$142$		0			0
$143$	1000.54	−	1732.98i	0.585099	−	1.01342i
$144$		0			0
$145$	420.320	+	728.015i	0.240729	+	0.416954i
$146$		0			0
$147$	1724.14	+	451.511i	0.967379	+	0.253333i
$148$		0			0
$149$	−569.751	+	986.838i	−0.313261	+	0.542583i	−0.979066	−	0.203542i	$-0.934755\pi$
$149$	−569.751	+	986.838i	−0.313261	+	0.542583i	0.665806	+	0.746125i	$0.268088\pi$
$150$		0			0
$151$	532.020	+	921.486i	0.286723	+	0.496619i	0.973026	−	0.230697i	$-0.0741007\pi$
$151$	532.020	+	921.486i	0.286723	+	0.496619i	−0.686303	+	0.727316i	$0.740767\pi$
$152$		0			0
$153$	−389.554	−	1130.45i	−0.205841	−	0.597328i
$154$		0			0
$155$	−745.429	+	1291.12i	−0.386286	+	0.669067i
$156$		0			0
$157$	−443.275			−0.225332			−0.112666	−	0.993633i	$-0.535939\pi$
$157$	−443.275			−0.225332			−0.112666	+	0.993633i	$0.535939\pi$
$158$		0			0
$159$	86.9797	−	904.483i	0.0433833	−	0.451133i
$160$		0			0
$161$	−1749.59	−	2055.10i	−0.856440	−	1.00599i
$162$		0			0
$163$	152.345	+	263.870i	0.0732061	+	0.126797i	0.900305	−	0.435260i	$-0.143344\pi$
$163$	152.345	+	263.870i	0.0732061	+	0.126797i	−0.827099	+	0.562057i	$0.810010\pi$
$164$		0			0
$165$	1793.16	−	817.458i	0.846046	−	0.385691i
$166$		0			0
$167$	1399.60	+	2424.17i	0.648527	+	1.12328i	0.983475	+	0.181045i	$0.0579478\pi$
$167$	1399.60	+	2424.17i	0.648527	+	1.12328i	−0.334948	+	0.942237i	$0.608719\pi$
$168$		0			0
$169$	−258.138	+	447.108i	−0.117496	+	0.203508i
$170$		0			0
$171$	664.791	+	129.053i	0.297297	+	0.0577129i
$172$		0			0
$173$	1689.98			0.742700			0.371350	−	0.928493i	$-0.378895\pi$
$173$	1689.98			0.742700			0.371350	+	0.928493i	$0.378895\pi$
$174$		0			0
$175$	−501.574	+	92.1379i	−0.216659	+	0.0397998i
$176$		0			0
$177$	−3895.60	+	1775.90i	−1.65430	+	0.754153i
$178$		0			0
$179$	−1798.60	+	3115.27i	−0.751028	+	1.30082i	0.196297	+	0.980544i	$0.437108\pi$
$179$	−1798.60	+	3115.27i	−0.751028	+	1.30082i	−0.947325	+	0.320274i	$0.896225\pi$
$180$		0			0
$181$	−2533.74			−1.04050			−0.520252	−	0.854013i	$-0.674162\pi$
$181$	−2533.74			−1.04050			−0.520252	+	0.854013i	$0.674162\pi$
$182$		0			0
$183$	2987.10	−	1361.74i	1.20663	−	0.550071i
$184$		0			0
$185$	2873.47			1.14196
$186$		0			0
$187$	−1701.25			−0.665283
$188$		0			0
$189$	−2100.22	−	1529.82i	−0.808300	−	0.588771i
$190$		0			0
$191$	−3405.76			−1.29022			−0.645110	−	0.764090i	$-0.723188\pi$
$191$	−3405.76			−1.29022			−0.645110	+	0.764090i	$0.723188\pi$
$192$		0			0
$193$	−827.630			−0.308674			−0.154337	−	0.988018i	$-0.549324\pi$
$193$	−827.630			−0.308674			−0.154337	+	0.988018i	$0.549324\pi$
$194$		0			0
$195$	−2431.37	+	1108.40i	−0.892891	+	0.407046i
$196$		0			0
$197$	2388.11			0.863685			0.431843	−	0.901949i	$-0.357864\pi$
$197$	2388.11			0.863685			0.431843	+	0.901949i	$0.357864\pi$
$198$		0			0
$199$	2589.31	−	4484.82i	0.922370	−	1.59759i	0.126633	−	0.991950i	$-0.459583\pi$
$199$	2589.31	−	4484.82i	0.922370	−	1.59759i	0.795737	−	0.605642i	$-0.207084\pi$
$200$		0			0
$201$	−2971.14	+	1354.47i	−1.04263	+	0.475308i
$202$		0			0
$203$	−1022.28	−	1200.79i	−0.353448	−	0.415167i
$204$		0			0
$205$	3029.62			1.03219
$206$		0			0
$207$	1281.94	+	3720.06i	0.430440	+	1.24909i
$208$		0			0
$209$	481.770	−	834.451i	0.159449	−	0.276173i
$210$		0			0
$211$	2520.38	+	4365.43i	0.822323	+	1.42431i	0.903948	+	0.427642i	$0.140656\pi$
$211$	2520.38	+	4365.43i	0.822323	+	1.42431i	−0.0816252	+	0.996663i	$0.526011\pi$
$212$		0			0
$213$	−2647.62	+	1206.98i	−0.851699	+	0.388268i
$214$		0			0
$215$	2635.18	+	4564.27i	0.835898	+	1.44782i
$216$		0			0
$217$	937.773	−	2634.89i	0.293365	−	0.824276i
$218$		0			0
$219$	−130.122	+	1353.11i	−0.0401498	+	0.417509i
$220$		0			0
$221$	2306.75			0.702120
$222$		0			0
$223$	487.947	−	845.149i	0.146526	−	0.253791i	−0.783415	−	0.621499i	$-0.786524\pi$
$223$	487.947	−	845.149i	0.146526	−	0.253791i	0.929941	+	0.367708i	$0.119857\pi$
$224$		0			0
$225$	729.836	+	141.680i	0.216248	+	0.0419792i
$226$		0			0
$227$	−1889.67	−	3273.01i	−0.552520	−	0.956992i	−0.998092	−	0.0617463i	$-0.980333\pi$
$227$	−1889.67	−	3273.01i	−0.552520	−	0.956992i	0.445572	−	0.895246i	$-0.353000\pi$
$228$		0			0
$229$	−2007.72	+	3477.48i	−0.579363	+	1.00349i	0.416190	+	0.909278i	$0.363365\pi$
$229$	−2007.72	+	3477.48i	−0.579363	+	1.00349i	−0.995553	+	0.0942082i	$0.969968\pi$
$230$		0			0
$231$	−3031.48	+	2116.05i	−0.863449	+	0.602711i
$232$		0			0
$233$	1899.28	+	3289.65i	0.534017	+	0.924944i	0.999210	+	0.0397352i	$0.0126514\pi$
$233$	1899.28	+	3289.65i	0.534017	+	0.924944i	−0.465193	+	0.885209i	$0.654015\pi$
$234$		0			0
$235$	−2299.28	+	3982.47i	−0.638248	+	1.10548i
$236$		0			0
$237$	−2753.20	+	1255.11i	−0.754596	+	0.344001i
$238$		0			0
$239$	−591.430	−	1024.39i	−0.160069	−	0.277247i	0.774824	−	0.632176i	$-0.217838\pi$
$239$	−591.430	−	1024.39i	−0.160069	−	0.277247i	−0.934893	+	0.354929i	$0.884505\pi$
$240$		0			0
$241$	523.396	+	906.549i	0.139896	+	0.242307i	0.927457	−	0.373930i	$-0.121990\pi$
$241$	523.396	+	906.549i	0.139896	+	0.242307i	−0.787561	+	0.616237i	$0.788657\pi$
$242$		0			0
$243$	2037.25	+	3193.51i	0.537817	+	0.843061i
$244$		0			0
$245$	−3165.16	+	1203.48i	−0.825366	+	0.313826i
$246$		0			0
$247$	−653.237	+	1131.44i	−0.168277	+	0.291465i
$248$		0			0
$249$	113.103	−	1176.14i	0.0287856	−	0.299335i
$250$		0			0
$251$	−4908.30			−1.23430			−0.617150	−	0.786846i	$-0.711713\pi$
$251$	−4908.30			−1.23430			−0.617150	+	0.786846i	$0.711713\pi$
$252$		0			0
$253$	5598.47			1.39120
$254$		0			0
$255$	1849.62	+	1318.98i	0.454226	+	0.323912i
$256$		0			0
$257$	1541.16	−	2669.36i	0.374065	−	0.647900i	−0.616121	−	0.787651i	$-0.711297\pi$
$257$	1541.16	−	2669.36i	0.374065	−	0.647900i	0.990187	+	0.139751i	$0.0446302\pi$
$258$		0			0
$259$	−5301.81	+	973.931i	−1.27196	+	0.233657i
$260$		0			0
$261$	749.035	+	2173.62i	0.177640	+	0.515493i
$262$		0			0
$263$	−2622.44	−	4542.19i	−0.614853	−	1.06496i	−0.990410	−	0.138157i	$-0.955882\pi$
$263$	−2622.44	−	4542.19i	−0.614853	−	1.06496i	0.375557	−	0.926799i	$-0.377451\pi$
$264$		0			0
$265$	863.198	+	1495.10i	0.200098	+	0.346579i
$266$		0			0
$267$	1307.36	+	932.291i	0.299661	+	0.213690i
$268$		0			0
$269$	−2900.24	+	5023.36i	−0.657363	+	1.13859i	0.323933	+	0.946080i	$0.394995\pi$
$269$	−2900.24	+	5023.36i	−0.657363	+	1.13859i	−0.981296	+	0.192506i	$0.938339\pi$
$270$		0			0
$271$	−643.457	−	1114.50i	−0.144233	−	0.249820i	0.784853	−	0.619682i	$-0.212738\pi$
$271$	−643.457	−	1114.50i	−0.144233	−	0.249820i	−0.929087	+	0.369862i	$0.879405\pi$
$272$		0			0
$273$	4110.41	−	2869.18i	0.911257	−	0.636083i
$274$		0			0
$275$	528.909	−	916.097i	0.115980	−	0.200883i
$276$		0			0
$277$	−4054.27	−	7022.20i	−0.879413	−	1.52319i	−0.851986	−	0.523565i	$-0.824602\pi$
$277$	−4054.27	−	7022.20i	−0.879413	−	1.52319i	−0.0274278	−	0.999624i	$-0.508732\pi$
$278$		0			0
$279$	−2674.22	+	3077.87i	−0.573840	+	0.660455i
$280$		0			0
$281$	1535.56	−	2659.67i	0.325993	−	0.564636i	−0.655720	−	0.755004i	$-0.727635\pi$
$281$	1535.56	−	2659.67i	0.325993	−	0.564636i	0.981713	+	0.190368i	$0.0609681\pi$
$282$		0			0
$283$	7937.59			1.66728			0.833641	−	0.552307i	$-0.186252\pi$
$283$	7937.59			1.66728			0.833641	+	0.552307i	$0.186252\pi$
$284$		0			0
$285$	−1170.73	+	533.707i	−0.243327	+	0.110927i
$286$		0			0
$287$	−5589.92	+	1026.86i	−1.14970	+	0.211197i
$288$		0			0
$289$	1475.94	+	2556.40i	0.300415	+	0.520333i
$290$		0			0
$291$	15.4135	−	160.282i	0.00310500	−	0.0322882i
$292$		0			0
$293$	−1352.93	−	2343.34i	−0.269757	−	0.467233i	0.699042	−	0.715081i	$-0.253610\pi$
$293$	−1352.93	−	2343.34i	−0.269757	−	0.467233i	−0.968799	+	0.247848i	$0.920277\pi$
$294$		0			0
$295$	4067.12	−	7044.46i	0.802701	−	1.39032i
$296$		0			0
$297$	5240.29	−	1260.12i	1.02381	−	0.246195i
$298$		0			0
$299$	−7591.01			−1.46823
$300$		0			0
$301$	−6409.16	−	7528.33i	−1.22730	−	1.44161i
$302$		0			0
$303$	5123.75	+	3653.78i	0.971457	+	0.692754i
$304$		0			0
$305$	−3118.62	+	5401.61i	−0.585482	+	1.01408i
$306$		0			0
$307$	−2802.90			−0.521075			−0.260537	−	0.965464i	$-0.583900\pi$
$307$	−2802.90			−0.521075			−0.260537	+	0.965464i	$0.583900\pi$
$308$		0			0
$309$	−176.580	+	1836.21i	−0.0325089	+	0.338053i
$310$		0			0
$311$	6881.55			1.25472			0.627358	−	0.778731i	$-0.284136\pi$
$311$	6881.55			1.25472			0.627358	+	0.778731i	$0.284136\pi$
$312$		0			0
$313$	4852.51			0.876295			0.438148	−	0.898903i	$-0.355635\pi$
$313$	4852.51			0.876295			0.438148	+	0.898903i	$0.355635\pi$
$314$		0			0
$315$	4936.42	+	49.7028i	0.882970	+	0.00889027i
$316$		0			0
$317$	−757.775			−0.134262			−0.0671308	−	0.997744i	$-0.521384\pi$
$317$	−757.775			−0.134262			−0.0671308	+	0.997744i	$0.521384\pi$
$318$		0			0
$319$	3271.17			0.574139
$320$		0			0
$321$	−2689.51	−	1917.91i	−0.467644	−	0.333481i
$322$		0			0
$323$	1110.73			0.191339
$324$		0			0
$325$	−717.152	+	1242.14i	−0.122401	+	0.212005i
$326$		0			0
$327$	797.622	−	8294.30i	0.134889	−	1.40268i
$328$		0			0
$329$	2892.56	−	8127.32i	0.484718	−	1.36193i
$330$		0			0
$331$	9645.75			1.60175			0.800874	−	0.598833i	$-0.204369\pi$
$331$	9645.75			1.60175			0.800874	+	0.598833i	$0.204369\pi$
$332$		0			0
$333$	7714.63	+	1497.61i	1.26955	+	0.246451i
$334$		0			0
$335$	3101.96	−	5372.75i	0.505905	−	0.876253i
$336$		0			0
$337$	−1486.08	−	2573.96i	−0.240213	−	0.416061i	0.720562	−	0.693391i	$-0.243884\pi$
$337$	−1486.08	−	2573.96i	−0.240213	−	0.416061i	−0.960775	+	0.277329i	$0.910551\pi$
$338$		0			0
$339$	−1464.03	−	1044.01i	−0.234557	−	0.167265i
$340$		0			0
$341$	2900.68	+	5024.13i	0.460647	+	0.797864i
$342$		0			0
$343$	5432.10	−	3293.32i	0.855118	−	0.518433i
$344$		0			0
$345$	−6086.70	−	4340.47i	−0.949846	−	0.677342i
$346$		0			0
$347$	−11920.3			−1.84413			−0.922065	−	0.387035i	$-0.873499\pi$
$347$	−11920.3			−1.84413			−0.922065	+	0.387035i	$0.873499\pi$
$348$		0			0
$349$	−4354.99	+	7543.07i	−0.667958	+	1.15694i	0.310516	+	0.950568i	$0.399498\pi$
$349$	−4354.99	+	7543.07i	−0.667958	+	1.15694i	−0.978474	+	0.206369i	$0.933835\pi$
$350$		0			0
$351$	−7105.35	+	1708.61i	−1.08050	+	0.259826i
$352$		0			0
$353$	−2877.06	−	4983.22i	−0.433798	−	0.751360i	0.563399	−	0.826185i	$-0.309494\pi$
$353$	−2877.06	−	4983.22i	−0.433798	−	0.751360i	−0.997197	+	0.0748250i	$0.976160\pi$
$354$		0			0
$355$	2764.19	−	4787.72i	0.413262	−	0.715791i
$356$		0			0
$357$	−3859.76	−	1806.72i	−0.572213	−	0.267848i
$358$		0			0
$359$	−3663.73	−	6345.77i	−0.538619	−	0.932916i	−0.998979	−	0.0451832i	$-0.985613\pi$
$359$	−3663.73	−	6345.77i	−0.538619	−	0.932916i	0.460360	−	0.887733i	$-0.347720\pi$
$360$		0			0
$361$	3114.96	−	5395.27i	0.454142	−	0.786597i
$362$		0			0
$363$	72.0314	−	749.038i	0.0104151	−	0.108304i
$364$		0			0
$365$	−1291.35	−	2236.68i	−0.185184	−	0.320748i
$366$		0			0
$367$	−2681.99	−	4645.35i	−0.381468	−	0.660723i	0.609804	−	0.792552i	$-0.291248\pi$
$367$	−2681.99	−	4645.35i	−0.381468	−	0.660723i	−0.991272	+	0.131830i	$0.957915\pi$
$368$		0			0
$369$	8133.86	+	1578.99i	1.14751	+	0.222761i
$370$		0			0
$371$	−2099.43	−	2466.03i	−0.293792	−	0.345094i
$372$		0			0
$373$	−767.341	+	1329.07i	−0.106519	+	0.184496i	−0.914358	−	0.404908i	$-0.867304\pi$
$373$	−767.341	+	1329.07i	−0.106519	+	0.184496i	0.807839	+	0.589403i	$0.200637\pi$
$374$		0			0
$375$	−7119.91	+	3245.79i	−0.980455	+	0.446965i
$376$		0			0
$377$	−4435.41			−0.605929
$378$		0			0
$379$	9580.55			1.29847			0.649235	−	0.760588i	$-0.275089\pi$
$379$	9580.55			1.29847			0.649235	+	0.760588i	$0.275089\pi$
$380$		0			0
$381$	8447.65	−	3851.07i	1.13592	−	0.517838i
$382$		0			0
$383$	330.433	−	572.328i	0.0440845	−	0.0763566i	−0.843141	−	0.537692i	$-0.819296\pi$
$383$	330.433	−	572.328i	0.0440845	−	0.0763566i	0.887226	+	0.461336i	$0.152630\pi$
$384$		0			0
$385$	2355.18	−	6617.41i	0.311769	−	0.875986i
$386$		0			0
$387$	4696.06	+	13627.5i	0.616832	+	1.78998i
$388$		0			0
$389$	6155.83	+	10662.2i	0.802347	+	1.38971i	0.918067	+	0.396424i	$0.129749\pi$
$389$	6155.83	+	10662.2i	0.802347	+	1.38971i	−0.115720	+	0.993282i	$0.536918\pi$
$390$		0			0
$391$	3226.83	+	5589.03i	0.417360	+	0.722888i
$392$		0			0
$393$	−594.201	+	6178.96i	−0.0762683	+	0.793098i
$394$		0			0
$395$	2874.42	−	4978.64i	0.366146	−	0.634183i
$396$		0			0
$397$	−38.7703	−	67.1521i	−0.00490132	−	0.00848934i	0.863564	−	0.504239i	$-0.168227\pi$
$397$	−38.7703	−	67.1521i	−0.00490132	−	0.00848934i	−0.868466	+	0.495749i	$0.834893\pi$
$398$		0			0
$399$	1979.21	−	1381.54i	0.248332	−	0.173342i
$400$		0			0
$401$	5024.11	−	8702.02i	0.625666	−	1.08369i	−0.362746	−	0.931888i	$-0.618161\pi$
$401$	5024.11	−	8702.02i	0.625666	−	1.08369i	0.988412	−	0.151797i	$-0.0485061\pi$
$402$		0			0
$403$	−3933.06	−	6812.26i	−0.486153	−	0.842042i
$404$		0			0
$405$	−6674.25	−	2692.76i	−0.818880	−	0.330381i
$406$		0			0
$407$	5590.75	−	9683.47i	0.680893	−	1.17934i
$408$		0			0
$409$	−4927.48			−0.595717			−0.297859	−	0.954610i	$-0.596272\pi$
$409$	−4927.48			−0.595717			−0.297859	+	0.954610i	$0.596272\pi$
$410$		0			0
$411$	52.8958	+	37.7204i	0.00634831	+	0.00452703i
$412$		0			0
$413$	−5116.56	+	14376.2i	−0.609611	+	1.71284i
$414$		0			0
$415$	1122.45	+	1944.14i	0.132769	+	0.229962i
$416$		0			0
$417$	7107.48	+	5068.40i	0.834664	+	0.595205i
$418$		0			0
$419$	−6794.86	−	11769.0i	−0.792245	−	1.37221i	−0.924574	−	0.381002i	$-0.875579\pi$
$419$	−6794.86	−	11769.0i	−0.792245	−	1.37221i	0.132329	−	0.991206i	$-0.457754\pi$
$420$		0			0
$421$	−6697.29	+	11600.1i	−0.775311	+	1.34288i	0.159308	+	0.987229i	$0.449074\pi$
$421$	−6697.29	+	11600.1i	−0.775311	+	1.34288i	−0.934619	+	0.355650i	$0.884260\pi$
$422$		0			0
$423$	−8248.64	+	9493.69i	−0.948139	+	1.09125i
$424$		0			0
$425$	1219.40			0.139176
$426$		0			0
$427$	3923.32	−	11023.5i	0.444644	−	1.24933i
$428$		0			0
$429$	−995.322	+	10350.1i	−0.112015	+	1.16482i
$430$		0			0
$431$	−4168.95	+	7220.83i	−0.465919	+	0.806995i	−0.999242	−	0.0389161i	$-0.987610\pi$
$431$	−4168.95	+	7220.83i	−0.465919	+	0.806995i	0.533324	+	0.845911i	$0.320943\pi$
$432$		0			0
$433$	8046.80			0.893082			0.446541	−	0.894763i	$-0.352656\pi$
$433$	8046.80			0.893082			0.446541	+	0.894763i	$0.352656\pi$
$434$		0			0
$435$	−3556.44	−	2536.13i	−0.391996	−	0.279535i
$436$		0			0
$437$	−3655.16			−0.400115
$438$		0			0
$439$	−3056.27			−0.332273			−0.166137	−	0.986103i	$-0.553129\pi$
$439$	−3056.27			−0.332273			−0.166137	+	0.986103i	$0.553129\pi$
$440$		0			0
$441$	−9124.98	+	1581.44i	−0.985312	+	0.170763i
$442$		0			0
$443$	−6477.52			−0.694709			−0.347355	−	0.937734i	$-0.612920\pi$
$443$	−6477.52			−0.694709			−0.347355	+	0.937734i	$0.612920\pi$
$444$		0			0
$445$	−3050.80			−0.324993
$446$		0			0
$447$	566.781	−	5893.84i	0.0599728	−	0.623644i
$448$		0			0
$449$	−3263.07			−0.342971			−0.171485	−	0.985187i	$-0.554857\pi$
$449$	−3263.07			−0.342971			−0.171485	+	0.985187i	$0.554857\pi$
$450$		0			0
$451$	5894.56	−	10209.7i	0.615442	−	1.06598i
$452$		0			0
$453$	−4501.57	−	3210.10i	−0.466892	−	0.332944i
$454$		0			0
$455$	−3193.41	+	8972.61i	−0.329031	+	0.924489i
$456$		0			0
$457$	−2243.43			−0.229635			−0.114817	−	0.993387i	$-0.536628\pi$
$457$	−2243.43			−0.229635			−0.114817	+	0.993387i	$0.536628\pi$
$458$		0			0
$459$	4278.38	+	4505.14i	0.435071	+	0.458131i
$460$		0			0
$461$	−731.687	+	1267.32i	−0.0739220	+	0.128037i	−0.900617	−	0.434614i	$-0.856885\pi$
$461$	−731.687	+	1267.32i	−0.0739220	+	0.128037i	0.826695	+	0.562650i	$0.190218\pi$
$462$		0			0
$463$	−2239.73	−	3879.33i	−0.224814	−	0.389390i	0.731449	−	0.681896i	$-0.238844\pi$
$463$	−2239.73	−	3879.33i	−0.224814	−	0.389390i	−0.956264	+	0.292506i	$0.905511\pi$
$464$		0			0
$465$	741.544	−	7711.16i	0.0739533	−	0.769024i
$466$		0			0
$467$	138.630	+	240.113i	0.0137366	+	0.0237925i	0.872812	−	0.488057i	$-0.162294\pi$
$467$	138.630	+	240.113i	0.0137366	+	0.0237925i	−0.859075	+	0.511849i	$0.828961\pi$
$468$		0			0
$469$	−3902.36	+	10964.6i	−0.384209	+	1.07952i
$470$		0			0
$471$	2095.82	−	955.430i	0.205032	−	0.0934690i
$472$		0			0
$473$	20508.5			1.99362
$474$		0			0
$475$	−345.317	+	598.107i	−0.0333563	+	0.0577748i
$476$		0			0
$477$	1538.27	+	4463.90i	0.147657	+	0.428486i
$478$		0			0
$479$	−3596.62	−	6229.53i	−0.343077	−	0.594227i	0.641925	−	0.766767i	$-0.278136\pi$
$479$	−3596.62	−	6229.53i	−0.343077	−	0.594227i	−0.985002	+	0.172540i	$0.944803\pi$
$480$		0			0
$481$	−7580.55	+	13129.9i	−0.718593	+	1.24464i
$482$		0			0
$483$	12701.7	+	5945.54i	1.19657	+	0.560106i
$484$		0			0
$485$	152.966	+	264.944i	0.0143213	+	0.0248051i
$486$		0			0
$487$	3384.91	−	5862.84i	0.314959	−	0.545525i	−0.664470	−	0.747315i	$-0.731343\pi$
$487$	3384.91	−	5862.84i	0.314959	−	0.545525i	0.979429	+	0.201790i	$0.0646760\pi$
$488$		0			0
$489$	−1289.03	−	919.221i	−0.119207	−	0.0850073i
$490$		0			0
$491$	5682.85	+	9842.98i	0.522329	+	0.904700i	0.999663	+	0.0259779i	$0.00826994\pi$
$491$	5682.85	+	9842.98i	0.522329	+	0.904700i	−0.477334	+	0.878722i	$0.658397\pi$
$492$		0			0
$493$	1885.43	+	3265.65i	0.172242	+	0.298332i
$494$		0			0
$495$	−6716.20	+	7729.93i	−0.609839	+	0.701888i
$496$		0			0
$497$	−3477.44	+	9770.66i	−0.313852	+	0.881839i
$498$		0			0
$499$	8391.35	−	14534.2i	0.752802	−	1.30389i	−0.193657	−	0.981069i	$-0.562035\pi$
$499$	8391.35	−	14534.2i	0.752802	−	1.30389i	0.946460	−	0.322822i	$-0.104632\pi$
$500$		0			0
$501$	−11842.4	−	8444.88i	−1.05604	−	0.753073i
$502$		0			0
$503$	19758.6			1.75148			0.875739	−	0.482784i	$-0.160374\pi$
$503$	19758.6			1.75148			0.875739	+	0.482784i	$0.160374\pi$
$504$		0			0
$505$	−11956.5			−1.05358
$506$		0			0
$507$	256.792	−	2670.33i	0.0224942	−	0.233912i
$508$		0			0
$509$	−134.260	+	232.546i	−0.0116915	+	0.0202503i	−0.871812	−	0.489841i	$-0.837055\pi$
$509$	−134.260	+	232.546i	−0.0116915	+	0.0202503i	0.860120	+	0.510091i	$0.170388\pi$
$510$		0			0
$511$	3140.74	+	3689.18i	0.271895	+	0.319373i
$512$		0			0
$513$	−3421.31	+	822.717i	−0.294453	+	0.0708067i
$514$		0			0
$515$	−1752.40	−	3035.24i	−0.149942	−	0.259706i
$516$		0			0
$517$	8947.15	+	15496.9i	0.761113	+	1.31829i
$518$		0			0
$519$	−7990.30	+	3642.57i	−0.675790	+	0.308076i
$520$		0			0
$521$	10087.3	−	17471.8i	0.848243	−	1.46920i	−0.0345321	−	0.999404i	$-0.510994\pi$
$521$	10087.3	−	17471.8i	0.848243	−	1.46920i	0.882775	−	0.469796i	$-0.155673\pi$
$522$		0			0
$523$	−1043.26	−	1806.97i	−0.0872246	−	0.151077i	0.819112	−	0.573633i	$-0.194466\pi$
$523$	−1043.26	−	1806.97i	−0.0872246	−	0.151077i	−0.906337	+	0.422556i	$0.861133\pi$
$524$		0			0
$525$	2172.86	−	1516.72i	0.180631	−	0.126086i
$526$		0			0
$527$	−3343.77	+	5791.58i	−0.276389	+	0.478719i
$528$		0			0
$529$	−4535.30	−	7855.38i	−0.372754	−	0.645630i
$530$		0			0
$531$	14590.8	−	16793.1i	1.19244	−	1.37242i
$532$		0			0
$533$	−7992.49	+	13843.4i	−0.649518	+	1.12500i
$534$		0			0
$535$	6276.11			0.507177
$536$		0			0
$537$	1789.23	−	18605.8i	0.143782	−	1.49516i
$538$		0			0
$539$	−2102.61	+	13008.0i	−0.168026	+	1.03951i
$540$		0			0
$541$	6638.17	+	11497.6i	0.527537	+	0.913720i	0.999485	+	0.0320939i	$0.0102176\pi$
$541$	6638.17	+	11497.6i	0.527537	+	0.913720i	−0.471948	+	0.881626i	$0.656449\pi$
$542$		0			0
$543$	11979.6	−	5461.19i	0.946766	−	0.431606i
$544$		0			0
$545$	7915.70	+	13710.4i	0.622150	+	1.07759i
$546$		0			0
$547$	−2452.05	+	4247.08i	−0.191668	+	0.331978i	−0.945803	−	0.324741i	$-0.894723\pi$
$547$	−2452.05	+	4247.08i	−0.191668	+	0.331978i	0.754135	+	0.656719i	$0.228056\pi$
$548$		0			0
$549$	−11188.0	+	12876.7i	−0.869752	+	1.00103i
$550$		0			0
$551$	−2135.70			−0.165125
$552$		0			0
$553$	−3616.10	+	10160.3i	−0.278069	+	0.781300i
$554$		0			0
$555$	−13585.9	+	6193.45i	−1.03908	+	0.473689i
$556$		0			0
$557$	−3018.73	+	5228.59i	−0.229637	+	0.397743i	−0.957700	−	0.287767i	$-0.907087\pi$
$557$	−3018.73	+	5228.59i	−0.229637	+	0.397743i	0.728064	+	0.685510i	$0.240421\pi$
$558$		0			0
$559$	−27807.7			−2.10401
$560$		0			0
$561$	8043.58	−	3666.87i	0.605348	−	0.275963i
$562$		0			0
$563$	4362.26			0.326549			0.163275	−	0.986581i	$-0.447794\pi$
$563$	4362.26			0.326549			0.163275	+	0.986581i	$0.447794\pi$
$564$		0			0
$565$	3416.38			0.254386
$566$		0			0
$567$	13227.3	+	2706.22i	0.979706	+	0.200442i
$568$		0			0
$569$	−21107.4			−1.55513			−0.777563	−	0.628805i	$-0.783544\pi$
$569$	−21107.4			−1.55513			−0.777563	+	0.628805i	$0.783544\pi$
$570$		0			0
$571$	−19963.7			−1.46314			−0.731572	−	0.681764i	$-0.761213\pi$
$571$	−19963.7			−1.46314			−0.731572	+	0.681764i	$0.761213\pi$
$572$		0			0
$573$	16102.5	−	7340.73i	1.17398	−	0.535189i
$574$		0			0
$575$	−4012.80			−0.291035
$576$		0			0
$577$	−8192.03	+	14189.0i	−0.591055	+	1.02374i	0.403036	+	0.915184i	$0.367955\pi$
$577$	−8192.03	+	14189.0i	−0.591055	+	1.02374i	−0.994091	+	0.108553i	$0.965378\pi$
$578$		0			0
$579$	3913.06	−	1783.87i	0.280866	−	0.128040i
$580$		0			0
$581$	−2729.97	−	3206.67i	−0.194936	−	0.228976i
$582$		0			0
$583$	6717.90			0.477234
$584$		0			0
$585$	9106.55	−	10481.1i	0.643606	−	0.740751i
$586$		0			0
$587$	9700.01	−	16800.9i	0.682048	−	1.18134i	−0.292306	−	0.956325i	$-0.594423\pi$
$587$	9700.01	−	16800.9i	0.682048	−	1.18134i	0.974355	−	0.225018i	$-0.0722440\pi$
$588$		0			0
$589$	−1893.81	−	3280.18i	−0.132484	−	0.229469i
$590$		0			0
$591$	−11291.1	+	5147.31i	−0.785876	+	0.358261i
$592$		0			0
$593$	6313.23	+	10934.8i	0.437189	+	0.757234i	0.997471	−	0.0710677i	$-0.0226406\pi$
$593$	6313.23	+	10934.8i	0.437189	+	0.757234i	−0.560282	+	0.828302i	$0.689307\pi$
$594$		0			0
$595$	7963.72	−	1462.92i	0.548707	−	0.100796i
$596$		0			0
$597$	−2575.82	+	26785.4i	−0.176585	+	1.83627i
$598$		0			0
$599$	−2181.08			−0.148776			−0.0743879	−	0.997229i	$-0.523700\pi$
$599$	−2181.08			−0.148776			−0.0743879	+	0.997229i	$0.523700\pi$
$600$		0			0
$601$	−6171.61	+	10689.5i	−0.418877	+	0.725517i	−0.995827	−	0.0912631i	$-0.970910\pi$
$601$	−6171.61	+	10689.5i	−0.418877	+	0.725517i	0.576950	+	0.816780i	$0.304243\pi$
$602$		0			0
$603$	11128.3	−	12807.9i	0.751538	−	0.864975i
$604$		0			0
$605$	714.849	+	1238.15i	0.0480376	+	0.0832035i
$606$		0			0
$607$	−8753.06	+	15160.7i	−0.585298	+	1.01377i	0.409541	+	0.912292i	$0.365689\pi$
$607$	−8753.06	+	15160.7i	−0.585298	+	1.01377i	−0.994838	+	0.101473i	$0.967644\pi$
$608$		0			0
$609$	7421.54	+	3473.96i	0.493819	+	0.231153i
$610$		0			0
$611$	−12131.5	−	21012.4i	−0.803255	−	1.39128i
$612$		0			0
$613$	−12199.8	+	21130.6i	−0.803823	+	1.39226i	0.113260	+	0.993565i	$0.463871\pi$
$613$	−12199.8	+	21130.6i	−0.803823	+	1.39226i	−0.917083	+	0.398696i	$0.869463\pi$
$614$		0			0
$615$	−14324.2	+	6530.02i	−0.939196	+	0.428156i
$616$		0			0
$617$	4811.03	+	8332.94i	0.313913	+	0.543714i	0.979206	−	0.202869i	$-0.0650265\pi$
$617$	4811.03	+	8332.94i	0.313913	+	0.543714i	−0.665292	+	0.746583i	$0.731693\pi$
$618$		0			0
$619$	12864.1	+	22281.2i	0.835299	+	1.44678i	0.893786	+	0.448493i	$0.148039\pi$
$619$	12864.1	+	22281.2i	0.835299	+	1.44678i	−0.0584871	+	0.998288i	$0.518628\pi$
$620$		0			0
$621$	−14079.2	−	14825.5i	−0.909791	−	0.958013i
$622$		0			0
$623$	5629.00	−	1034.03i	0.361992	−	0.0664971i
$624$		0			0
$625$	5712.42	−	9894.21i	0.365595	−	0.633229i
$626$		0			0
$627$	−479.259	+	4983.71i	−0.0305260	+	0.317433i
$628$		0			0
$629$	12889.5			0.817073
$630$		0			0
$631$	−6874.40			−0.433702			−0.216851	−	0.976205i	$-0.569579\pi$
$631$	−6874.40			−0.433702			−0.216851	+	0.976205i	$0.569579\pi$
$632$		0			0
$633$	−21325.6	−	15207.5i	−1.33905	−	0.954886i
$634$		0			0
$635$	−8819.59	+	15276.0i	−0.551173	+	0.954659i
$636$		0			0
$637$	2850.95	−	17637.6i	0.177329	−	1.09706i
$638$		0			0
$639$	9916.51	−	11413.3i	0.613914	−	0.706578i
$640$		0			0
$641$	3110.37	+	5387.31i	0.191657	+	0.331960i	0.945799	−	0.324751i	$-0.105281\pi$
$641$	3110.37	+	5387.31i	0.191657	+	0.331960i	−0.754143	+	0.656711i	$0.771947\pi$
$642$		0			0
$643$	10417.6	+	18043.7i	0.638924	+	1.10665i	0.985669	+	0.168689i	$0.0539535\pi$
$643$	10417.6	+	18043.7i	0.638924	+	1.10665i	−0.346745	+	0.937959i	$0.612713\pi$
$644$		0			0
$645$	−22297.0	−	15900.2i	−1.36115	−	0.970650i
$646$		0			0
$647$	−4148.63	+	7185.63i	−0.252086	+	0.436625i	−0.964100	−	0.265540i	$-0.914450\pi$
$647$	−4148.63	+	7185.63i	−0.252086	+	0.436625i	0.712014	+	0.702165i	$0.247783\pi$
$648$		0			0
$649$	−15826.3	−	27412.0i	−0.957223	−	1.65796i
$650$		0			0
$651$	1245.39	+	14479.1i	0.0749783	+	0.871707i
$652$		0			0
$653$	15822.2	−	27404.9i	0.948194	−	1.64232i	0.198968	−	0.980006i	$-0.436241\pi$
$653$	15822.2	−	27404.9i	0.948194	−	1.64232i	0.749226	−	0.662315i	$-0.230426\pi$
$654$		0			0
$655$	−5896.93	−	10213.8i	−0.351774	−	0.609290i
$656$		0			0
$657$	−2301.25	−	6678.00i	−0.136652	−	0.396550i
$658$		0			0
$659$	697.693	−	1208.44i	0.0412417	−	0.0714326i	−0.844668	−	0.535291i	$-0.820202\pi$
$659$	697.693	−	1208.44i	0.0412417	−	0.0714326i	0.885909	+	0.463858i	$0.153535\pi$
$660$		0			0
$661$	−7090.09			−0.417205			−0.208603	−	0.978000i	$-0.566892\pi$
$661$	−7090.09			−0.417205			−0.208603	+	0.978000i	$0.566892\pi$
$662$		0			0
$663$	−10906.4	+	4971.94i	−0.638866	+	0.291243i
$664$		0			0
$665$	−1537.66	+	4320.42i	−0.0896661	+	0.251938i
$666$		0			0
$667$	−6204.54	−	10746.6i	−0.360181	−	0.623852i
$668$		0			0
$669$	−485.404	+	5047.61i	−0.0280520	+	0.291707i
$670$		0			0
$671$	12135.5	+	21019.2i	0.698188	+	1.20930i
$672$		0			0
$673$	−8005.93	+	13866.7i	−0.458553	+	0.794237i	−0.998885	−	0.0472154i	$-0.984965\pi$
$673$	−8005.93	+	13866.7i	−0.458553	+	0.794237i	0.540332	+	0.841452i	$0.318299\pi$
$674$		0			0
$675$	−3756.06	+	903.215i	−0.214179	+	0.0515034i
$676$		0			0
$677$	24421.9			1.38642			0.693212	−	0.720733i	$-0.256195\pi$
$677$	24421.9			1.38642			0.693212	+	0.720733i	$0.256195\pi$
$678$		0			0
$679$	−372.035	−	436.999i	−0.0210271	−	0.0246988i
$680$		0			0
$681$	15989.0	+	11401.9i	0.899709	+	0.641589i
$682$		0			0
$683$	15188.2	−	26306.8i	0.850895	−	1.47379i	−0.0295058	−	0.999565i	$-0.509393\pi$
$683$	15188.2	−	26306.8i	0.850895	−	1.47379i	0.880401	−	0.474230i	$-0.157273\pi$
$684$		0			0
$685$	−123.435			−0.00688498
$686$		0			0
$687$	1997.26	−	20769.1i	0.110917	−	1.15341i
$688$		0			0
$689$	−9108.87			−0.503658
$690$		0			0
$691$	13796.1			0.759522			0.379761	−	0.925085i	$-0.376006\pi$
$691$	13796.1			0.759522			0.379761	+	0.925085i	$0.376006\pi$
$692$		0			0
$693$	9772.00	−	16538.8i	0.535653	−	0.906575i
$694$		0			0
$695$	−16585.7			−0.905223
$696$		0			0
$697$	13590.0			0.738531
$698$		0			0
$699$	−16070.3	−	11459.9i	−0.869579	−	0.620104i
$700$		0			0
$701$	25916.9			1.39639			0.698194	−	0.715909i	$-0.253987\pi$
$701$	25916.9			1.39639			0.698194	+	0.715909i	$0.253987\pi$
$702$		0			0
$703$	−3650.12	+	6322.20i	−0.195828	+	0.339184i
$704$		0			0
$705$	2287.29	−	23785.1i	0.122191	−	1.27064i
$706$		0			0
$707$	22060.8	−	4052.53i	1.17353	−	0.215574i
$708$		0			0
$709$	28876.6			1.52960			0.764799	−	0.644269i	$-0.222838\pi$
$709$	28876.6			1.52960			0.764799	+	0.644269i	$0.222838\pi$
$710$		0			0
$711$	10311.9	−	11868.4i	0.543922	−	0.626021i
$712$		0			0
$713$	11003.6	−	19058.9i	0.577966	−	1.00107i
$714$		0			0
$715$	−9877.71	−	17108.7i	−0.516651	−	0.894866i
$716$		0			0
$717$	5004.25	+	3568.57i	0.260652	+	0.185873i
$718$		0			0
$719$	2549.42	+	4415.72i	0.132235	+	0.229038i	0.924538	−	0.381090i	$-0.124451\pi$
$719$	2549.42	+	4415.72i	0.132235	+	0.229038i	−0.792303	+	0.610128i	$0.791118\pi$
$720$		0			0
$721$	4262.09	+	5006.34i	0.220151	+	0.258593i
$722$		0			0
$723$	−4428.60	−	3158.07i	−0.227803	−	0.162448i
$724$		0			0
$725$	−2344.67			−0.120109
$726$		0			0
$727$	−14557.3	+	25214.0i	−0.742643	+	1.28629i	0.208645	+	0.977991i	$0.433095\pi$
$727$	−14557.3	+	25214.0i	−0.742643	+	1.28629i	−0.951288	+	0.308304i	$0.900239\pi$
$728$		0			0
$729$	−16515.4	−	10708.0i	−0.839072	−	0.544021i
$730$		0			0
$731$	11820.6	+	20473.9i	0.598088	+	1.03592i
$732$		0			0
$733$	8413.88	−	14573.3i	0.423975	−	0.734347i	−0.572349	−	0.820010i	$-0.693968\pi$
$733$	8413.88	−	14573.3i	0.423975	−	0.734347i	0.996324	+	0.0856635i	$0.0273010\pi$
$734$		0			0
$735$	12371.0	−	12512.2i	0.620832	−	0.627919i
$736$		0			0
$737$	−12070.6	−	20906.9i	−0.603293	−	1.04493i
$738$		0			0
$739$	−660.500	+	1144.02i	−0.0328781	+	0.0569465i	−0.881996	−	0.471256i	$-0.843801\pi$
$739$	−660.500	+	1144.02i	−0.0328781	+	0.0569465i	0.849118	+	0.528203i	$0.177134\pi$
$740$		0			0
$741$	649.832	−	6757.46i	0.0322162	−	0.335009i
$742$		0			0
$743$	−2416.51	−	4185.51i	−0.119318	−	0.206664i	0.800180	−	0.599760i	$-0.204737\pi$
$743$	−2416.51	−	4185.51i	−0.119318	−	0.206664i	−0.919497	+	0.393096i	$0.871404\pi$
$744$		0			0
$745$	5624.81	+	9742.47i	0.276614	+	0.479109i
$746$		0			0
$747$	2000.27	+	5804.59i	0.0979735	+	0.284309i
$748$		0			0
$749$	−11580.0	+	2127.22i	−0.564917	+	0.103774i
$750$		0			0
$751$	15703.1	−	27198.6i	0.763004	−	1.32156i	−0.178292	−	0.983978i	$-0.557057\pi$
$751$	15703.1	−	27198.6i	0.763004	−	1.32156i	0.941296	−	0.337583i	$-0.109610\pi$
$752$		0			0
$753$	23206.6	−	10579.3i	1.12310	−	0.511993i
$754$		0			0
$755$	10504.6			0.506361
$756$		0			0
$757$	6010.05			0.288559			0.144279	−	0.989537i	$-0.453914\pi$
$757$	6010.05			0.288559			0.144279	+	0.989537i	$0.453914\pi$
$758$		0			0
$759$	−26469.7	+	12066.9i	−1.26586	+	0.577075i
$760$		0			0
$761$	18611.2	−	32235.6i	0.886539	−	1.53553i	0.0426000	−	0.999092i	$-0.486436\pi$
$761$	18611.2	−	32235.6i	0.886539	−	1.53553i	0.843939	−	0.536439i	$-0.180231\pi$
$762$		0			0
$763$	−19252.2	−	22614.0i	−0.913467	−	1.07298i
$764$		0			0
$765$	−11588.0	−	2249.52i	−0.547665	−	0.106316i
$766$		0			0
$767$	21459.1	+	37168.2i	1.01022	+	1.74976i
$768$		0			0
$769$	−15103.7	−	26160.3i	−0.708261	−	1.22674i	−0.965502	−	0.260396i	$-0.916147\pi$
$769$	−15103.7	−	26160.3i	−0.708261	−	1.22674i	0.257241	−	0.966347i	$-0.417187\pi$
$770$		0			0
$771$	−1533.13	+	15942.6i	−0.0716137	+	0.744695i
$772$		0			0
$773$	−2031.30	+	3518.32i	−0.0945160	+	0.163706i	−0.909407	−	0.415908i	$-0.863464\pi$
$773$	−2031.30	+	3518.32i	−0.0945160	+	0.163706i	0.814891	+	0.579615i	$0.196797\pi$
$774$		0			0
$775$	−2079.11	−	3601.13i	−0.0963663	−	0.166911i
$776$		0			0
$777$	22967.9	−	16032.2i	1.06045	−	0.740224i
$778$		0			0
$779$	−3848.48	+	6665.76i	−0.177004	+	0.306580i
$780$		0			0
$781$	−10756.3	−	18630.4i	−0.492816	−	0.853582i
$782$		0			0
$783$	−8226.46	−	8662.49i	−0.375466	−	0.395367i
$784$		0			0
$785$	−2188.09	+	3789.89i	−0.0994859	+	0.172315i
$786$		0			0
$787$	−789.724			−0.0357695			−0.0178848	−	0.999840i	$-0.505693\pi$
$787$	−789.724			−0.0357695			−0.0178848	+	0.999840i	$0.505693\pi$
$788$		0			0
$789$	22189.2	+	15823.3i	1.00121	+	0.713971i
$790$		0			0
$791$	−6303.52	+	1157.94i	−0.283347	+	0.0520502i
$792$		0			0
$793$	−16454.6	−	28500.2i	−0.736847	−	1.27626i
$794$		0			0
$795$	−7303.76	−	5208.37i	−0.325834	−	0.232354i
$796$		0			0
$797$	14442.2	+	25014.7i	0.641870	+	1.11175i	0.985015	+	0.172468i	$0.0551743\pi$
$797$	14442.2	+	25014.7i	0.641870	+	1.11175i	−0.343145	+	0.939282i	$0.611492\pi$
$798$		0			0
$799$	−10313.9	+	17864.1i	−0.456669	+	0.790973i
$800$		0			0
$801$	−8190.71	−	1590.03i	−0.361304	−	0.0701383i
$802$		0			0
$803$	−10050.0			−0.441664
$804$		0			0
$805$	−26206.9	+	4814.16i	−1.14742	+	0.210778i
$806$		0			0
$807$	2885.12	−	30001.7i	0.125850	−	1.30869i
$808$		0			0
$809$	−2245.50	+	3889.33i	−0.0975868	+	0.169025i	−0.910685	−	0.413101i	$-0.864446\pi$
$809$	−2245.50	+	3889.33i	−0.0975868	+	0.169025i	0.813099	+	0.582126i	$0.197779\pi$
$810$		0			0
$811$	2023.63			0.0876195			0.0438098	−	0.999040i	$-0.486050\pi$
$811$	2023.63			0.0876195			0.0438098	+	0.999040i	$0.486050\pi$
$812$		0			0
$813$	5444.47	+	3882.50i	0.234866	+	0.167485i
$814$		0			0
$815$	3008.03			0.129284
$816$		0			0
$817$	−13389.7			−0.573375
$818$		0			0
$819$	−13250.0	+	22425.1i	−0.565312	+	0.956772i
$820$		0			0
$821$	14901.7			0.633462			0.316731	−	0.948515i	$-0.397415\pi$
$821$	14901.7			0.633462			0.316731	+	0.948515i	$0.397415\pi$
$822$		0			0
$823$	−10133.5			−0.429200			−0.214600	−	0.976702i	$-0.568845\pi$
$823$	−10133.5			−0.429200			−0.214600	+	0.976702i	$0.568845\pi$
$824$		0			0
$825$	−526.152	+	5471.34i	−0.0222039	+	0.230894i
$826$		0			0
$827$	−31703.2			−1.33305			−0.666523	−	0.745485i	$-0.732218\pi$
$827$	−31703.2			−1.33305			−0.666523	+	0.745485i	$0.732218\pi$
$828$		0			0
$829$	−22869.7	+	39611.5i	−0.958140	+	1.65955i	−0.231126	+	0.972924i	$0.574241\pi$
$829$	−22869.7	+	39611.5i	−0.958140	+	1.65955i	−0.727014	+	0.686623i	$0.759092\pi$
$830$		0			0
$831$	34304.3	+	24462.7i	1.43201	+	1.02118i
$832$		0			0
$833$	−14197.9	+	5398.43i	−0.590552	+	0.224543i
$834$		0			0
$835$	27634.8			1.14532
$836$		0			0
$837$	6009.80	−	20316.2i	0.248183	−	0.838987i
$838$		0			0
$839$	10135.1	−	17554.5i	0.417047	−	0.722346i	−0.578594	−	0.815616i	$-0.696398\pi$
$839$	10135.1	−	17554.5i	0.417047	−	0.722346i	0.995641	+	0.0932694i	$0.0297318\pi$
$840$		0			0
$841$	8569.21	+	14842.3i	0.351355	+	0.608565i
$842$		0			0
$843$	−1527.56	+	15884.8i	−0.0624103	+	0.648992i
$844$		0			0
$845$	2548.44	+	4414.03i	0.103750	+	0.179701i
$846$		0			0
$847$	−1738.62	−	2042.22i	−0.0705308	−	0.0828469i
$848$		0			0
$849$	−37529.2	+	17108.6i	−1.51708	+	0.691597i
$850$		0			0
$851$	−42416.7			−1.70861
$852$		0			0
$853$	1276.41	−	2210.81i	0.0512351	−	0.0887417i	−0.839270	−	0.543714i	$-0.817018\pi$
$853$	1276.41	−	2210.81i	0.0512351	−	0.0887417i	0.890506	+	0.454972i	$0.150351\pi$
$854$		0			0
$855$	4384.91	−	5046.77i	0.175393	−	0.201866i
$856$		0			0
$857$	1452.79	+	2516.31i	0.0579072	+	0.100298i	0.893526	−	0.449012i	$-0.148224\pi$
$857$	1452.79	+	2516.31i	0.0579072	+	0.100298i	−0.835619	+	0.549310i	$0.814891\pi$
$858$		0			0
$859$	−14166.5	+	24537.1i	−0.562695	+	0.974615i	0.434566	+	0.900640i	$0.356902\pi$
$859$	−14166.5	+	24537.1i	−0.562695	+	0.974615i	−0.997260	+	0.0739753i	$0.976431\pi$
$860$		0			0
$861$	24216.1	−	16903.5i	0.958515	−	0.669069i
$862$		0			0
$863$	−25011.4	−	43321.1i	−0.986558	−	1.70877i	−0.634799	−	0.772678i	$-0.718917\pi$
$863$	−25011.4	−	43321.1i	−0.986558	−	1.70877i	−0.351759	−	0.936091i	$-0.614416\pi$
$864$		0			0
$865$	8342.10	−	14448.9i	0.327908	−	0.567952i
$866$		0			0
$867$	−12488.3	−	8905.51i	−0.489187	−	0.348843i
$868$		0			0
$869$	−11185.2	−	19373.3i	−0.436630	−	0.756265i
$870$		0			0
$871$	16366.7	+	28347.9i	0.636697	+	1.10279i
$872$		0			0
$873$	272.594	+	791.038i	0.0105680	+	0.0306673i
$874$		0			0
$875$	−9351.43	+	26275.0i	−0.361299	+	1.01515i
$876$		0			0
$877$	−3542.46	+	6135.72i	−0.136397	+	0.236247i	−0.926130	−	0.377204i	$-0.876886\pi$
$877$	−3542.46	+	6135.72i	−0.136397	+	0.236247i	0.789733	+	0.613451i	$0.210219\pi$
$878$		0			0
$879$	11447.5	+	8163.29i	0.439265	+	0.313244i
$880$		0			0
$881$	36559.2			1.39808			0.699041	−	0.715082i	$-0.253611\pi$
$881$	36559.2			1.39808			0.699041	+	0.715082i	$0.253611\pi$
$882$		0			0
$883$	24587.0			0.937055			0.468528	−	0.883449i	$-0.344785\pi$
$883$	24587.0			0.937055			0.468528	+	0.883449i	$0.344785\pi$
$884$		0			0
$885$	−4045.92	+	42072.6i	−0.153675	+	1.59803i
$886$		0			0
$887$	−14833.7	+	25692.7i	−0.561518	+	0.972577i	0.435847	+	0.900021i	$0.356449\pi$
$887$	−14833.7	+	25692.7i	−0.561518	+	0.972577i	−0.997364	+	0.0725561i	$0.976884\pi$
$888$		0			0
$889$	11095.3	−	31174.8i	0.418588	−	1.17612i
$890$		0			0
$891$	−22060.2	+	17252.8i	−0.829455	+	0.648698i
$892$		0			0
$893$	−5841.47	−	10117.7i	−0.218900	−	0.379145i
$894$		0			0
$895$	17756.5	+	30755.2i	0.663169	+	1.14864i
$896$		0			0
$897$	35890.6	−	16361.6i	1.33595	−	0.609028i
$898$		0			0
$899$	6429.40	−	11136.0i	0.238523	−	0.413134i
$900$		0			0
$901$	3872.04	+	6706.58i	0.143170	+	0.247978i
$902$		0			0
$903$	46529.2	+	21779.9i	1.71472	+	0.802647i
$904$		0			0
$905$	−12507.0	+	21662.8i	−0.459390	+	0.795687i
$906$		0			0
$907$	4622.56	+	8006.51i	0.169228	+	0.293111i	0.938149	−	0.346233i	$-0.112539\pi$
$907$	4622.56	+	8006.51i	0.169228	+	0.293111i	−0.768921	+	0.639344i	$0.779206\pi$
$908$		0			0
$909$	−32100.6	−	6231.54i	−1.17130	−	0.227378i
$910$		0			0
$911$	20898.8	−	36197.8i	0.760053	−	1.31645i	−0.182769	−	0.983156i	$-0.558506\pi$
$911$	20898.8	−	36197.8i	0.760053	−	1.31645i	0.942823	−	0.333295i	$-0.108160\pi$
$912$		0			0
$913$	8735.56			0.316654
$914$		0			0
$915$	3102.37	−	32260.9i	0.112089	−	1.16559i
$916$		0			0
$917$	14342.2	+	16846.6i	0.516490	+	0.606679i
$918$		0			0
$919$	14177.6	+	24556.4i	0.508898	+	0.881437i	0.999947	+	0.0103050i	$0.00328025\pi$
$919$	14177.6	+	24556.4i	0.508898	+	0.881437i	−0.491049	+	0.871132i	$0.663386\pi$
$920$		0			0
$921$	13252.2	−	6041.34i	0.474131	−	0.216144i
$922$		0			0
$923$	14584.5	+	25261.1i	0.520103	+	0.900845i
$924$		0			0
$925$	−4007.27	+	6940.79i	−0.142441	+	0.246715i
$926$		0			0
$927$	−3122.88	−	9062.27i	−0.110646	−	0.321083i
$928$		0			0
$929$	−16914.8			−0.597370			−0.298685	−	0.954352i	$-0.596548\pi$
$929$	−16914.8			−0.597370			−0.298685	+	0.954352i	$0.596548\pi$
$930$		0			0
$931$	1372.77	−	8492.73i	0.0483250	−	0.298967i
$932$		0			0
$933$	−32536.2	+	14832.4i	−1.14168	+	0.520462i
$934$		0			0
$935$	−8397.74	+	14545.3i	−0.293728	+	0.508751i
$936$		0			0
$937$	54255.3			1.89161			0.945807	−	0.324728i	$-0.105273\pi$
$937$	54255.3			1.89161			0.945807	+	0.324728i	$0.105273\pi$
$938$		0			0
$939$	−22942.8	+	10459.1i	−0.797350	+	0.363492i
$940$		0			0
$941$	−52914.6			−1.83312			−0.916561	−	0.399896i	$-0.869046\pi$
$941$	−52914.6			−1.83312			−0.916561	+	0.399896i	$0.869046\pi$
$942$		0			0
$943$	−44721.7			−1.54437
$944$		0			0
$945$	−23446.7	+	10404.9i	−0.807111	+	0.358171i
$946$		0			0
$947$	−1433.71			−0.0491969			−0.0245984	−	0.999697i	$-0.507831\pi$
$947$	−1433.71			−0.0491969			−0.0245984	+	0.999697i	$0.507831\pi$
$948$		0			0
$949$	13626.9			0.466119
$950$		0			0
$951$	3582.79	−	1633.30i	0.122166	−	0.0556924i
$952$		0			0
$953$	51163.6			1.73909			0.869544	−	0.493856i	$-0.164413\pi$
$953$	51163.6			1.73909			0.869544	+	0.493856i	$0.164413\pi$
$954$		0			0
$955$	−16811.5	+	29118.4i	−0.569641	+	0.986648i
$956$		0			0
$957$	−15466.2	+	7050.64i	−0.522415	+	0.238156i
$958$		0			0
$959$	227.749	−	41.8369i	0.00766880	−	0.00140874i
$960$		0			0
$961$	−6986.16			−0.234506
$962$		0			0
$963$	16849.9	+	3271.00i	0.563844	+	0.109456i
$964$		0			0
$965$	−4085.35	+	7076.03i	−0.136282	+	0.236047i
$966$		0			0
$967$	4495.41	+	7786.28i	0.149496	+	0.258935i	0.931041	−	0.364914i	$-0.118902\pi$
$967$	4495.41	+	7786.28i	0.149496	+	0.258935i	−0.781545	+	0.623848i	$0.785568\pi$
$968$		0			0
$969$	−5251.54	+	2394.05i	−0.174101	+	0.0793682i
$970$		0			0
$971$	−14623.9	−	25329.3i	−0.483318	−	0.837132i	0.516498	−	0.856288i	$-0.327235\pi$
$971$	−14623.9	−	25329.3i	−0.483318	−	0.837132i	−0.999816	+	0.0191565i	$0.993902\pi$
$972$		0			0
$973$	30602.0	−	5621.52i	1.00828	−	0.185219i
$974$		0			0
$975$	713.414	−	7418.64i	0.0234334	−	0.243679i
$976$		0			0
$977$	−53592.8			−1.75495			−0.877475	−	0.479623i	$-0.840773\pi$
$977$	−53592.8			−1.75495			−0.877475	+	0.479623i	$0.840773\pi$
$978$		0			0
$979$	−5935.77	+	10281.1i	−0.193777	+	0.335632i
$980$		0			0
$981$	14106.3	+	40934.9i	0.459101	+	1.33226i
$982$		0			0
$983$	4326.39	+	7493.53i	0.140377	+	0.243140i	0.927639	−	0.373479i	$-0.121835\pi$
$983$	4326.39	+	7493.53i	0.140377	+	0.243140i	−0.787262	+	0.616619i	$0.788502\pi$
$984$		0			0
$985$	11788.2	−	20417.8i	0.381323	−	0.660471i
$986$		0			0
$987$	3841.42	+	44660.8i	0.123884	+	1.44029i
$988$		0			0
$989$	−38899.2	−	67375.4i	−1.25068	−	2.16624i
$990$		0			0
$991$	21012.1	−	36394.0i	0.673533	−	1.16659i	−0.303362	−	0.952875i	$-0.598109\pi$
$991$	21012.1	−	36394.0i	0.673533	−	1.16659i	0.976895	−	0.213718i	$-0.0685575\pi$
$992$		0			0
$993$	−45605.4	+	20790.4i	−1.45745	+	0.664413i
$994$		0			0
$995$	−25562.8	−	44276.0i	−0.814466	−	1.41070i
$996$		0			0
$997$	−24306.5	−	42100.2i	−0.772112	−	1.33734i	−0.936403	−	0.350926i	$-0.885867\pi$
$997$	−24306.5	−	42100.2i	−0.772112	−	1.33734i	0.164291	−	0.986412i	$-0.447466\pi$
$998$		0			0
$999$	−39702.9	+	9547.31i	−1.25740	+	0.302366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.3	✓	48
3.2	odd	2		756.4.i.a.613.6		48
7.2	even	3		252.4.l.a.205.13	yes	48
9.4	even	3		252.4.l.a.193.13	yes	48
9.5	odd	6		756.4.l.a.361.19		48
21.2	odd	6		756.4.l.a.289.19		48
63.23	odd	6		756.4.i.a.37.6		48
63.58	even	3	inner	252.4.i.a.121.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.3	✓	48	1.1	even	1	trivial
252.4.i.a.121.3	yes	48	63.58	even	3	inner
252.4.l.a.193.13	yes	48	9.4	even	3
252.4.l.a.205.13	yes	48	7.2	even	3
756.4.i.a.37.6		48	63.23	odd	6
756.4.i.a.613.6		48	3.2	odd	2
756.4.l.a.289.19		48	21.2	odd	6
756.4.l.a.361.19		48	9.5	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.72803 + 2.15539i) q^{3} +(4.93620 - 8.54976i) q^{5} +(-6.20989 + 17.4481i) q^{7} +(17.7086 - 20.3815i) q^{9} +O(q^{10})\)	\(q+(-4.72803 + 2.15539i) q^{3} +(4.93620 - 8.54976i) q^{5} +(-6.20989 + 17.4481i) q^{7} +(17.7086 - 20.3815i) q^{9} +(-19.2082 - 33.2696i) q^{11} +(26.0446 + 45.1105i) q^{13} +(-4.91047 + 51.0630i) q^{15} +(22.1423 - 38.3516i) q^{17} +(12.5408 + 21.7212i) q^{19} +(-8.24695 - 95.8801i) q^{21} +(-72.8656 + 126.207i) q^{23} +(13.7678 + 23.8465i) q^{25} +(-39.7967 + 134.533i) q^{27} +(-42.5752 + 73.7424i) q^{29} -151.013 q^{31} +(162.526 + 115.898i) q^{33} +(118.524 + 139.221i) q^{35} +(145.530 + 252.066i) q^{37} +(-220.370 - 157.148i) q^{39} +(153.439 + 265.764i) q^{41} +(-266.924 + 462.326i) q^{43} +(-86.8437 - 252.011i) q^{45} -465.799 q^{47} +(-265.874 - 216.702i) q^{49} +(-22.0269 + 229.053i) q^{51} +(-87.4354 + 151.443i) q^{53} -379.262 q^{55} +(-106.111 - 75.6685i) q^{57} +823.937 q^{59} -631.786 q^{61} +(245.651 + 435.549i) q^{63} +514.245 q^{65} +628.410 q^{67} +(72.4859 - 753.765i) q^{69} +559.983 q^{71} +(130.803 - 226.558i) q^{73} +(-116.493 - 83.0721i) q^{75} +(699.772 - 128.547i) q^{77} +582.313 q^{79} +(-101.812 - 721.855i) q^{81} +(-113.696 + 196.927i) q^{83} +(-218.598 - 378.623i) q^{85} +(42.3533 - 440.423i) q^{87} +(-154.511 - 267.622i) q^{89} +(-948.828 + 174.298i) q^{91} +(713.993 - 325.491i) q^{93} +247.615 q^{95} +(-15.4942 + 26.8368i) q^{97} +(-1018.23 - 197.665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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